1In the state of Hawaii license plates consist of 4 capital

1.In the state of Hawaii license plates consist of 4 capital letters followed by 3 digits.
a.How many license plates are possible?
b.What is the probability that a random plate begins with the letter X?
c.What is the probability that a random plate begins with the letter X and ends in a 9?

Solution

1a)

There are 26^4 possible letter combinations, and 10^3 number combinations.

Thus, there are 26^4*10^3 = 456976000 [answer]

b)

The choices of each letter and number are all independent. Thus, as there are 26 letters for the first letter,

P(starts with x) = P(x) = 1/26 [answer]

c)

The choices of each letter and number are all independent. Thus, as there are 26 letters for the first letter, and 10 digits for the last digit,

P(starts with x, ends with 9) = P(x) P(9) = (1/26)(1/10) = 1/260 [answer]