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![[Post New]](/templates/default/images/icon_minipost_new.gif) 12 Jul 2007 16:35:03 IST
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wat is the probability dat a digit in a car's (4 digit) registration no. will be repeated: (a)only twice (b)only thrice (c)all 4 digits are same (plz explain in full detail)
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12 Jul 2007 17:25:39 IST
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Since we are talking about a car's registration number, the beginning digits can be zero (s) [ for e.g registration number 0123, 0001 or 0015, etc ]
Each place of the four digit number can be filled up in 10 ways i.e 0 to 9
Total such four digit numbers that are possible are = 10 4
(a) When same digit occurs twice
Two places can be selected from four-digit no. in 4C2 ways and the repetitive digit can be sel. in 10 ways & the remaining two places can be filled up in 9 x 8 = 72 ways since the repeated digit can't be selected again.
Total such four digit numbers that are possible whose same digit occurs twice
= 72 x 4C2 x 10
Total probability = 72 x 4C2 / 10 3
(b) When same digit occurs thrice
3 places can be selected from four-digit no. in 4C3 ways and the repetitive digit can be sel. in 10 ways & the remaining 1 place can be filled up in 9 ways.
Total such four digit numbers that are possible whose same digit occurs twice
= 9 x 4C3
Total probability = 9 x 4C3 / 10 3
(c) When the same digit occupies all the four places.
Only one such number is possible and the repetitive digit can be sel. in 10 ways
Total probability = 10 / 10 4 = 1 / 10 3
Cheers !!!!!
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You never know what is enough till you know what is more than enough.
Titun |
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12 Jul 2007 17:58:17 IST
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Titun's is a good approach. however, there is a rider as below.
(a) for 2 digit case :
There are 4c2 ways of choosing 2 places for a repetitive digit and that digit can be anyone of the 10. Hence, the probability =
[(10*1*9*9)*(4c2)] / 10^4 = [4c2 * 9^2] /10^3 . denom is 10^3 not 10^ 4 as above.
Similarly for 3 digit case, the ans is [4c3 * 9]/10^3
similarly for 4 digit case, the ans is [1/ 10^3]. rgds.
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12 Jul 2007 18:16:40 IST
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One more rider. for the two digit case as below.
2 nos are to repeat and the other two are not to repeat. Hence
Prob = [(10*1*9*8)*(4c2)] / 10^4 = [4c2 * 9 * 8] / 10^3 and not as above. The other cases are just fine.
Hope i donot come bask with another rider. Rgds.
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