(c) How many different seven-place license plates are possible if repetition is

Question

(c) How many different seven-place license plates are possible if repetition is allowed? Assume that first three places are taken from the alphabet (total 26) and the last four places are taken from the integers {0, 1, . . . , 9} (total 10), e.g. SSS7777 is available. (Hint: the all cases of 3-digit number from {1, 2, . . . , 9}, when repetition is allowed, e.g. 911, counts 9 × 9 × 9 = 729.) (d) Assuming (c), what is the probability of having ABC in the first three-place? Given the first three-place equals ABC, what is the conditional probability of the last four numbers are even?

Explanation / Answer

c)

___ ___ ___ ___ ___ ___ ___

26 26 26 10 10 10 10

So total no of ways = 26^3 * 10^4

d)

Since first 3 rows are filled, now the no of ways is 1*1*1*10^4

Sp probablity = 10^4/ 26^3 * 10^4 = 1/26^4

e)

No of ways to have ABC and 4 evennumbers is 1*1*1*5^4

So conditional probablity is 5^4/10^4 = 1/16

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