Question: 2022 Winter Final - 2
Consider strings of length $70$, in which each character is one of the characters $a,b,c,d,e$. How many such strings have exactly $5$ letters $a$ and exactly $15$ letters $b$?
(a)
$\binom{70}{5}\cdot\binom{65}{15}\cdot 4^{50}$
(b)
$\binom{70}{5}\cdot\binom{65}{15}\cdot 3^{50}$
(c)
$\binom{70}{5}\cdot\binom{65}{15}\cdot 5^{50}$
(d)
$\binom{70}{5}\cdot\binom{70}{15}\cdot 3^{50}$
(e)
$\binom{70}{15}\cdot\binom{55}{5}\cdot 5^{50}$