A computer program generates random strings consisting of five letters, which are chosen from any of the following seven: a, g, j, o, x, y, z, with repetitions allowed. Answer the following:
a) How many different strings are possible?
b) How many different strings are there that contain two or more identical letters?
c) What is the probability of a string having no letter ‘a’ and containing two or more identical letters?
a) $7^5 = 16807$
b) $7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 = 2520$
$16807 - 2520 = 14287$