Question: 2022 Winter Final - 4
Consider strings of length $70$, in which each character is one of the characters $a,b,c,d,e$. How many such strings have at least $10$ letters $a$?
(a)
$\binom{70}{10}\cdot 5^{60}$
(b)
$\sum_{i=10}^{70} \binom{70}{i}\cdot 5^{70-i}$
(c)
$\binom{70}{10}\cdot 4^{60}$
(d)
None of the above
(e)
$5^{70} - \sum_{i=0}^{9} \binom{70}{i}\cdot 4^{70-i}$