How many different $7$-digit numbers can be formed from $0,1,2,2,3,3,3$ assuming no number can start with $0$? How many numbers will end with $0$? [on hold]

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I got this question and wanted to confirm my solution.




How many different $7$-digit numbers can be formed from $0,1,2,2,3,3,3$ assuming no number can start with $0$? How many numbers will end with $0$?




For the first part, I got $360$, and for part 2, I got $60$.



Did I do this correctly?




combinatorics permutations




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put on hold as off-topic by Henrik, Ennar, Jendrik Stelzner, Brahadeesh, Xander Henderson 11 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Henrik, Ennar, Jendrik Stelzner, Brahadeesh, Xander Henderson
If this question can be reworded to fit the rules in the help center, please edit the question.








  • 2




    would you like to show us your working?
    – Siong Thye Goh
    yesterday






  • 1




    It's hard to tell if you did it correctly when we don't know how you did it. We can answer whether you got the right results, but if you got those by rolling dice, that's not really worth anything.
    – Henrik
    yesterday














up vote
0
down vote

favorite












I got this question and wanted to confirm my solution.




How many different $7$-digit numbers can be formed from $0,1,2,2,3,3,3$ assuming no number can start with $0$? How many numbers will end with $0$?




For the first part, I got $360$, and for part 2, I got $60$.



Did I do this correctly?




combinatorics permutations




share|cite|improve this question













put on hold as off-topic by Henrik, Ennar, Jendrik Stelzner, Brahadeesh, Xander Henderson 11 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Henrik, Ennar, Jendrik Stelzner, Brahadeesh, Xander Henderson
If this question can be reworded to fit the rules in the help center, please edit the question.








  • 2




    would you like to show us your working?
    – Siong Thye Goh
    yesterday






  • 1




    It's hard to tell if you did it correctly when we don't know how you did it. We can answer whether you got the right results, but if you got those by rolling dice, that's not really worth anything.
    – Henrik
    yesterday












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I got this question and wanted to confirm my solution.




How many different $7$-digit numbers can be formed from $0,1,2,2,3,3,3$ assuming no number can start with $0$? How many numbers will end with $0$?




For the first part, I got $360$, and for part 2, I got $60$.



Did I do this correctly?




combinatorics permutations




share|cite|improve this question













I got this question and wanted to confirm my solution.




How many different $7$-digit numbers can be formed from $0,1,2,2,3,3,3$ assuming no number can start with $0$? How many numbers will end with $0$?




For the first part, I got $360$, and for part 2, I got $60$.



Did I do this correctly?





combinatorics permutations





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited yesterday









N. F. Taussig

37.9k92953




37.9k92953









asked yesterday









user122343

445




445




put on hold as off-topic by Henrik, Ennar, Jendrik Stelzner, Brahadeesh, Xander Henderson 11 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Henrik, Ennar, Jendrik Stelzner, Brahadeesh, Xander Henderson
If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by Henrik, Ennar, Jendrik Stelzner, Brahadeesh, Xander Henderson 11 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Henrik, Ennar, Jendrik Stelzner, Brahadeesh, Xander Henderson
If this question can be reworded to fit the rules in the help center, please edit the question.







  • 2




    would you like to show us your working?
    – Siong Thye Goh
    yesterday






  • 1




    It's hard to tell if you did it correctly when we don't know how you did it. We can answer whether you got the right results, but if you got those by rolling dice, that's not really worth anything.
    – Henrik
    yesterday












  • 2




    would you like to show us your working?
    – Siong Thye Goh
    yesterday






  • 1




    It's hard to tell if you did it correctly when we don't know how you did it. We can answer whether you got the right results, but if you got those by rolling dice, that's not really worth anything.
    – Henrik
    yesterday







2




2




would you like to show us your working?
– Siong Thye Goh
yesterday




would you like to show us your working?
– Siong Thye Goh
yesterday




1




1




It's hard to tell if you did it correctly when we don't know how you did it. We can answer whether you got the right results, but if you got those by rolling dice, that's not really worth anything.
– Henrik
yesterday




It's hard to tell if you did it correctly when we don't know how you did it. We can answer whether you got the right results, but if you got those by rolling dice, that's not really worth anything.
– Henrik
yesterday










2 Answers
2






active

oldest

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up vote
0
down vote



accepted










Yes, those answers are correct. The answer for $1$) is



$$
frac7!-6!3!cdot2!=360;,
$$



and the answer for $2$) is



$$
frac6!3!cdot2!=60;.
$$






share|cite|improve this answer




























    up vote
    0
    down vote













    Yes, the answers you got are correct.



    This can be solved as follows



    $a)$ $2$ is repeated $2$ times and $3$ is repeated $3$ times in the given digits.



    So, the number of ways $7$ digit numbers are $=dfrac7!2!times3!=420$



    Number of ways of forming $7$ digit numbers having $0$ at the beginning is $=dfrac6!2!times3!=60$



    Therefore, total number of numbers that begin with $0$ are $420-60=360$



    $b)$ Similarly, since $2$ is repeated $2$ times and $3$ is repeated $3$ times in the given digits.



    So, the number of ways $7$ digit numbers are $=dfrac7!2!times3!=420$






    share|cite|improve this answer




























      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes








      up vote
      0
      down vote



      accepted










      Yes, those answers are correct. The answer for $1$) is



      $$
      frac7!-6!3!cdot2!=360;,
      $$



      and the answer for $2$) is



      $$
      frac6!3!cdot2!=60;.
      $$






      share|cite|improve this answer

























        up vote
        0
        down vote



        accepted










        Yes, those answers are correct. The answer for $1$) is



        $$
        frac7!-6!3!cdot2!=360;,
        $$



        and the answer for $2$) is



        $$
        frac6!3!cdot2!=60;.
        $$






        share|cite|improve this answer























          up vote
          0
          down vote



          accepted







          up vote
          0
          down vote



          accepted






          Yes, those answers are correct. The answer for $1$) is



          $$
          frac7!-6!3!cdot2!=360;,
          $$



          and the answer for $2$) is



          $$
          frac6!3!cdot2!=60;.
          $$






          share|cite|improve this answer













          Yes, those answers are correct. The answer for $1$) is



          $$
          frac7!-6!3!cdot2!=360;,
          $$



          and the answer for $2$) is



          $$
          frac6!3!cdot2!=60;.
          $$







          share|cite|improve this answer













          share|cite|improve this answer



          share|cite|improve this answer











          answered yesterday









          joriki

          164k10179328




          164k10179328




















              up vote
              0
              down vote













              Yes, the answers you got are correct.



              This can be solved as follows



              $a)$ $2$ is repeated $2$ times and $3$ is repeated $3$ times in the given digits.



              So, the number of ways $7$ digit numbers are $=dfrac7!2!times3!=420$



              Number of ways of forming $7$ digit numbers having $0$ at the beginning is $=dfrac6!2!times3!=60$



              Therefore, total number of numbers that begin with $0$ are $420-60=360$



              $b)$ Similarly, since $2$ is repeated $2$ times and $3$ is repeated $3$ times in the given digits.



              So, the number of ways $7$ digit numbers are $=dfrac7!2!times3!=420$






              share|cite|improve this answer

























                up vote
                0
                down vote













                Yes, the answers you got are correct.



                This can be solved as follows



                $a)$ $2$ is repeated $2$ times and $3$ is repeated $3$ times in the given digits.



                So, the number of ways $7$ digit numbers are $=dfrac7!2!times3!=420$



                Number of ways of forming $7$ digit numbers having $0$ at the beginning is $=dfrac6!2!times3!=60$



                Therefore, total number of numbers that begin with $0$ are $420-60=360$



                $b)$ Similarly, since $2$ is repeated $2$ times and $3$ is repeated $3$ times in the given digits.



                So, the number of ways $7$ digit numbers are $=dfrac7!2!times3!=420$






                share|cite|improve this answer























                  up vote
                  0
                  down vote










                  up vote
                  0
                  down vote









                  Yes, the answers you got are correct.



                  This can be solved as follows



                  $a)$ $2$ is repeated $2$ times and $3$ is repeated $3$ times in the given digits.



                  So, the number of ways $7$ digit numbers are $=dfrac7!2!times3!=420$



                  Number of ways of forming $7$ digit numbers having $0$ at the beginning is $=dfrac6!2!times3!=60$



                  Therefore, total number of numbers that begin with $0$ are $420-60=360$



                  $b)$ Similarly, since $2$ is repeated $2$ times and $3$ is repeated $3$ times in the given digits.



                  So, the number of ways $7$ digit numbers are $=dfrac7!2!times3!=420$






                  share|cite|improve this answer













                  Yes, the answers you got are correct.



                  This can be solved as follows



                  $a)$ $2$ is repeated $2$ times and $3$ is repeated $3$ times in the given digits.



                  So, the number of ways $7$ digit numbers are $=dfrac7!2!times3!=420$



                  Number of ways of forming $7$ digit numbers having $0$ at the beginning is $=dfrac6!2!times3!=60$



                  Therefore, total number of numbers that begin with $0$ are $420-60=360$



                  $b)$ Similarly, since $2$ is repeated $2$ times and $3$ is repeated $3$ times in the given digits.



                  So, the number of ways $7$ digit numbers are $=dfrac7!2!times3!=420$







                  share|cite|improve this answer













                  share|cite|improve this answer



                  share|cite|improve this answer











                  answered yesterday









                  Key Flex

                  3,613322




                  3,613322












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