Number of permutations of $3$ t-shirts out of $4$

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Mr. A has a set of $4$ distinct t-shirts. Since it is winter he has to wear $3$ t-shirts everyday to beat the cold. How many distinct arrangements of t-shirts can he wear anyday? (Here is he has t-shirts $a$,$b$,$c$ and $d$ then wearing $a$ inside of $b$ which is inside $c$ is different than wearing $c$ inside of $b$ which is inside of $a$.




Clearly this question just involves choosing three t-shirts and finding out their permutations. This can be done in $4 choose 3 cdot 3! = 24$ ways. But the source from which I got this question from has the answer as $48$. Am I going wrong somewhere?




combinatorics permutations




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Mr. A has a set of $4$ distinct t-shirts. Since it is winter he has to wear $3$ t-shirts everyday to beat the cold. How many distinct arrangements of t-shirts can he wear anyday? (Here is he has t-shirts $a$,$b$,$c$ and $d$ then wearing $a$ inside of $b$ which is inside $c$ is different than wearing $c$ inside of $b$ which is inside of $a$.




Clearly this question just involves choosing three t-shirts and finding out their permutations. This can be done in $4 choose 3 cdot 3! = 24$ ways. But the source from which I got this question from has the answer as $48$. Am I going wrong somewhere?




combinatorics permutations




share|cite|improve this question





















  • you are right and the book is wrong
    – WW1
    2 days ago












up vote
1
down vote

favorite









up vote
1
down vote

favorite












Mr. A has a set of $4$ distinct t-shirts. Since it is winter he has to wear $3$ t-shirts everyday to beat the cold. How many distinct arrangements of t-shirts can he wear anyday? (Here is he has t-shirts $a$,$b$,$c$ and $d$ then wearing $a$ inside of $b$ which is inside $c$ is different than wearing $c$ inside of $b$ which is inside of $a$.




Clearly this question just involves choosing three t-shirts and finding out their permutations. This can be done in $4 choose 3 cdot 3! = 24$ ways. But the source from which I got this question from has the answer as $48$. Am I going wrong somewhere?




combinatorics permutations




share|cite|improve this question














Mr. A has a set of $4$ distinct t-shirts. Since it is winter he has to wear $3$ t-shirts everyday to beat the cold. How many distinct arrangements of t-shirts can he wear anyday? (Here is he has t-shirts $a$,$b$,$c$ and $d$ then wearing $a$ inside of $b$ which is inside $c$ is different than wearing $c$ inside of $b$ which is inside of $a$.




Clearly this question just involves choosing three t-shirts and finding out their permutations. This can be done in $4 choose 3 cdot 3! = 24$ ways. But the source from which I got this question from has the answer as $48$. Am I going wrong somewhere?





combinatorics permutations





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edited 2 days ago









N. F. Taussig

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asked 2 days ago









Helix

1227




1227











  • you are right and the book is wrong
    – WW1
    2 days ago
















  • you are right and the book is wrong
    – WW1
    2 days ago















you are right and the book is wrong
– WW1
2 days ago




you are right and the book is wrong
– WW1
2 days ago










1 Answer
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I suspect that the source meant that he needs to wear at least $3$ T-shirts. That's $24$ arrangements of $3$ T-shirts, as you calculated, and another $4!=24$ arrangements of all $4$ T-shirts.






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  • Thanks! I didn't think this way...
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1 Answer
1






active

oldest

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active

oldest

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up vote
1
down vote



accepted










I suspect that the source meant that he needs to wear at least $3$ T-shirts. That's $24$ arrangements of $3$ T-shirts, as you calculated, and another $4!=24$ arrangements of all $4$ T-shirts.






share|cite|improve this answer





















  • Thanks! I didn't think this way...
    – Helix
    yesterday














up vote
1
down vote



accepted










I suspect that the source meant that he needs to wear at least $3$ T-shirts. That's $24$ arrangements of $3$ T-shirts, as you calculated, and another $4!=24$ arrangements of all $4$ T-shirts.






share|cite|improve this answer





















  • Thanks! I didn't think this way...
    – Helix
    yesterday












up vote
1
down vote



accepted







up vote
1
down vote



accepted






I suspect that the source meant that he needs to wear at least $3$ T-shirts. That's $24$ arrangements of $3$ T-shirts, as you calculated, and another $4!=24$ arrangements of all $4$ T-shirts.






share|cite|improve this answer













I suspect that the source meant that he needs to wear at least $3$ T-shirts. That's $24$ arrangements of $3$ T-shirts, as you calculated, and another $4!=24$ arrangements of all $4$ T-shirts.







share|cite|improve this answer













share|cite|improve this answer



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answered 2 days ago









joriki

164k10179328




164k10179328











  • Thanks! I didn't think this way...
    – Helix
    yesterday
















  • Thanks! I didn't think this way...
    – Helix
    yesterday















Thanks! I didn't think this way...
– Helix
yesterday




Thanks! I didn't think this way...
– Helix
yesterday












 

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