Question: 2018 Fall Final - 2
Consider strings of length 70, in which each character is one of the letters $a, b, c$. How many
such strings have exactly 12 letters $c$ and exactly 30 letters $b$?
(a)
${70 \choose 12} \cdot {58 \choose 30} \cdot 3^{28}$
(b)
${70 \choose 12} \cdot {58 \choose 30} \cdot 2^{28}$
(c)
${70 \choose 12} \cdot {58 \choose 30}$
(d)
${70 \choose 12} + {58 \choose 30}$