Question: 2019 Winter Final - 1
Consider strings of length 85, in which each character is one of the letters $a, b, c, d$.
How many such strings have exactly 5 letters $c$?
(a)
${85 \choose 5} \cdot 3^{85}$
(b)
${85 \choose 5} \cdot 3^{80}$
(c)
${85 \choose 5} \cdot 4^{80}$
(d)
${85 \choose 5} \cdot 4^{85}$