Mixing
Permutations problem of counting license plates of entire country
Clash Royale CLAN TAG#URR8PPP
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I read lot of archives already but this permutation problem is a bit different. I want to count total number of license plates my country can have. It has this 4-part format : "2 Letters (State Title) - 2 Digits - 2 Letters - 4 Digits"
It has to follow these conditions:
part #1 is State Title, there are total 37 in number (29 states and 7 union territories + one state holds 2 titles). They look like TS, AP, PB etc. you can't just have any 2 letters. It is a fixed number, 37.
part #2, which is 2 digits, can be any digit but not "00", can be "01" and "10", "99" etc but 2 zeroes can't be together.
part #3, it has 2 letters but 1 state (Delhi, capital of the country) has 3 letter system and for 3rd letter we are limited to 8 choices of S,C,E,P,R,T,V,Y.
part #4, 4 digits, it can not be all zeroes, 4 zeroes can't be together.
I came up with this:
- part #1 = 37
- part #2 = 10*9 = 90
- part #3 = 28 states follow 2 letters (26*26) while 1 state follows 3 letters with first 2 letters as 26*26 and a 3rd letter as 8 choices. How to compute this ? Unknown number 'X'
- part #4 = 10*10*10*9 = 9000
Total number of license plates India can have: 37 *90 * X * 9000 . I need to know how to calculate X.
You can see state titles here:
https://upload.wikimedia.org/wikipedia/commons/thumb/5/59/IndiaStatesByRTOcodes.png/878px-IndiaStatesByRTOcodes.png
combinatorics permutations
asked Jul 24 at 4:30
Arnuld
4510
add a comment |Â
up vote
1
down vote
favorite
I read lot of archives already but this permutation problem is a bit different. I want to count total number of license plates my country can have. It has this 4-part format : "2 Letters (State Title) - 2 Digits - 2 Letters - 4 Digits"
It has to follow these conditions:
part #1 is State Title, there are total 37 in number (29 states and 7 union territories + one state holds 2 titles). They look like TS, AP, PB etc. you can't just have any 2 letters. It is a fixed number, 37.
part #2, which is 2 digits, can be any digit but not "00", can be "01" and "10", "99" etc but 2 zeroes can't be together.
part #3, it has 2 letters but 1 state (Delhi, capital of the country) has 3 letter system and for 3rd letter we are limited to 8 choices of S,C,E,P,R,T,V,Y.
part #4, 4 digits, it can not be all zeroes, 4 zeroes can't be together.
I came up with this:
- part #1 = 37
- part #2 = 10*9 = 90
- part #3 = 28 states follow 2 letters (26*26) while 1 state follows 3 letters with first 2 letters as 26*26 and a 3rd letter as 8 choices. How to compute this ? Unknown number 'X'
- part #4 = 10*10*10*9 = 9000
Total number of license plates India can have: 37 *90 * X * 9000 . I need to know how to calculate X.
You can see state titles here:
https://upload.wikimedia.org/wikipedia/commons/thumb/5/59/IndiaStatesByRTOcodes.png/878px-IndiaStatesByRTOcodes.png
combinatorics permutations
asked Jul 24 at 4:30
Arnuld
4510
You should specify that Delhi is not the state that holds two titles.
– N. F. Taussig
Jul 24 at 7:36
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I read lot of archives already but this permutation problem is a bit different. I want to count total number of license plates my country can have. It has this 4-part format : "2 Letters (State Title) - 2 Digits - 2 Letters - 4 Digits"
It has to follow these conditions:
part #1 is State Title, there are total 37 in number (29 states and 7 union territories + one state holds 2 titles). They look like TS, AP, PB etc. you can't just have any 2 letters. It is a fixed number, 37.
part #2, which is 2 digits, can be any digit but not "00", can be "01" and "10", "99" etc but 2 zeroes can't be together.
part #3, it has 2 letters but 1 state (Delhi, capital of the country) has 3 letter system and for 3rd letter we are limited to 8 choices of S,C,E,P,R,T,V,Y.
part #4, 4 digits, it can not be all zeroes, 4 zeroes can't be together.
I came up with this:
- part #1 = 37
- part #2 = 10*9 = 90
- part #3 = 28 states follow 2 letters (26*26) while 1 state follows 3 letters with first 2 letters as 26*26 and a 3rd letter as 8 choices. How to compute this ? Unknown number 'X'
- part #4 = 10*10*10*9 = 9000
Total number of license plates India can have: 37 *90 * X * 9000 . I need to know how to calculate X.
You can see state titles here:
https://upload.wikimedia.org/wikipedia/commons/thumb/5/59/IndiaStatesByRTOcodes.png/878px-IndiaStatesByRTOcodes.png
combinatorics permutations
asked Jul 24 at 4:30
Arnuld
4510
I read lot of archives already but this permutation problem is a bit different. I want to count total number of license plates my country can have. It has this 4-part format : "2 Letters (State Title) - 2 Digits - 2 Letters - 4 Digits"
It has to follow these conditions:
part #1 is State Title, there are total 37 in number (29 states and 7 union territories + one state holds 2 titles). They look like TS, AP, PB etc. you can't just have any 2 letters. It is a fixed number, 37.
part #2, which is 2 digits, can be any digit but not "00", can be "01" and "10", "99" etc but 2 zeroes can't be together.
part #3, it has 2 letters but 1 state (Delhi, capital of the country) has 3 letter system and for 3rd letter we are limited to 8 choices of S,C,E,P,R,T,V,Y.
part #4, 4 digits, it can not be all zeroes, 4 zeroes can't be together.
I came up with this:
- part #1 = 37
- part #2 = 10*9 = 90
- part #3 = 28 states follow 2 letters (26*26) while 1 state follows 3 letters with first 2 letters as 26*26 and a 3rd letter as 8 choices. How to compute this ? Unknown number 'X'
- part #4 = 10*10*10*9 = 9000
Total number of license plates India can have: 37 *90 * X * 9000 . I need to know how to calculate X.
You can see state titles here:
https://upload.wikimedia.org/wikipedia/commons/thumb/5/59/IndiaStatesByRTOcodes.png/878px-IndiaStatesByRTOcodes.png
combinatorics permutations
asked Jul 24 at 4:30
Arnuld
4510
asked Jul 24 at 4:30
Arnuld
4510
asked Jul 24 at 4:30
Arnuld
4510
asked Jul 24 at 4:30
Arnuld
4510
4510
You should specify that Delhi is not the state that holds two titles.
– N. F. Taussig
Jul 24 at 7:36
add a comment |Â
You should specify that Delhi is not the state that holds two titles.
– N. F. Taussig
Jul 24 at 7:36
You should specify that Delhi is not the state that holds two titles.
– N. F. Taussig
Jul 24 at 7:36
You should specify that Delhi is not the state that holds two titles.
– N. F. Taussig
Jul 24 at 7:36
add a comment |Â
1 Answer
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For part $2$, it sounds like there are $99$ possibilities-all the two digit strings except $00$. You need to compute part $1$ and part $3$ together. The number of possibilities are $36cdot 26^2+1cdot 26^2cdot 8$ where the first term accounts for all the non-Delhi areas where there are $36$ choices for the state or territory and $26^2$ choices for the letters and the second accounts for Delhi. Again, it sounds like part $4$ has $9999$ possibilities if $0000$ is the only excluded one. The full calculation is then $$99 cdot (36cdot 26^2+1cdot 26^2cdot 8)cdot 9999$$
If I have misinterpreted part $2$ or $4$ you can change them back.
answered Jul 24 at 4:46
Ross Millikan
275k21186351
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
For part $2$, it sounds like there are $99$ possibilities-all the two digit strings except $00$. You need to compute part $1$ and part $3$ together. The number of possibilities are $36cdot 26^2+1cdot 26^2cdot 8$ where the first term accounts for all the non-Delhi areas where there are $36$ choices for the state or territory and $26^2$ choices for the letters and the second accounts for Delhi. Again, it sounds like part $4$ has $9999$ possibilities if $0000$ is the only excluded one. The full calculation is then $$99 cdot (36cdot 26^2+1cdot 26^2cdot 8)cdot 9999$$
If I have misinterpreted part $2$ or $4$ you can change them back.
answered Jul 24 at 4:46
Ross Millikan
275k21186351
add a comment |Â
up vote
1
down vote
For part $2$, it sounds like there are $99$ possibilities-all the two digit strings except $00$. You need to compute part $1$ and part $3$ together. The number of possibilities are $36cdot 26^2+1cdot 26^2cdot 8$ where the first term accounts for all the non-Delhi areas where there are $36$ choices for the state or territory and $26^2$ choices for the letters and the second accounts for Delhi. Again, it sounds like part $4$ has $9999$ possibilities if $0000$ is the only excluded one. The full calculation is then $$99 cdot (36cdot 26^2+1cdot 26^2cdot 8)cdot 9999$$
If I have misinterpreted part $2$ or $4$ you can change them back.
answered Jul 24 at 4:46
Ross Millikan
275k21186351
add a comment |Â
up vote
1
down vote
up vote
1
down vote
For part $2$, it sounds like there are $99$ possibilities-all the two digit strings except $00$. You need to compute part $1$ and part $3$ together. The number of possibilities are $36cdot 26^2+1cdot 26^2cdot 8$ where the first term accounts for all the non-Delhi areas where there are $36$ choices for the state or territory and $26^2$ choices for the letters and the second accounts for Delhi. Again, it sounds like part $4$ has $9999$ possibilities if $0000$ is the only excluded one. The full calculation is then $$99 cdot (36cdot 26^2+1cdot 26^2cdot 8)cdot 9999$$
If I have misinterpreted part $2$ or $4$ you can change them back.
answered Jul 24 at 4:46
Ross Millikan
275k21186351
For part $2$, it sounds like there are $99$ possibilities-all the two digit strings except $00$. You need to compute part $1$ and part $3$ together. The number of possibilities are $36cdot 26^2+1cdot 26^2cdot 8$ where the first term accounts for all the non-Delhi areas where there are $36$ choices for the state or territory and $26^2$ choices for the letters and the second accounts for Delhi. Again, it sounds like part $4$ has $9999$ possibilities if $0000$ is the only excluded one. The full calculation is then $$99 cdot (36cdot 26^2+1cdot 26^2cdot 8)cdot 9999$$
If I have misinterpreted part $2$ or $4$ you can change them back.
answered Jul 24 at 4:46
Ross Millikan
275k21186351
answered Jul 24 at 4:46
Ross Millikan
275k21186351
answered Jul 24 at 4:46
Ross Millikan
275k21186351
answered Jul 24 at 4:46
Ross Millikan
275k21186351
275k21186351
add a comment |Â
add a comment |Â
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You should specify that Delhi is not the state that holds two titles.
– N. F. Taussig
Jul 24 at 7:36