Question: 2019 Winter Final - 2
Consider strings of length 85, in which each character is one of the letters $a, b, c, d$.
How many such strings have exactly 15 letters $a$ and exactly 30 letters $d$?
(a)
${85 \choose 15} \cdot {70 \choose 30} \cdot 3^{40}$
(b)
${85 \choose 15} \cdot {70 \choose 30} \cdot 4^{40}$
(c)
${85 \choose 15} \cdot {70 \choose 30} \cdot 2^{40}$
(d)
None of the above.