Practice By Tag: Permutations and Binomial Coefficients

Question: 2019 Fall Final - 1

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)

${85 \choose 5} \cdot 3^{80}$

(b)

${85 \choose 5} \cdot 4^{80}$

(c)

${85 \choose 5} \cdot 3^{85}$

(d)

${85 \choose 5} \cdot 4^{85}$