Question: 2019 Fall Final - 3
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 $a$ or exactly 30 letters $d$?
How many such strings have exactly 15 letters $a$ or exactly 30 letters $d$?
(a)
None of the above.
(b)
${85 \choose 15} \cdot 3^{70} + {85 \choose 30} \cdot 3^{55}$
(c)
${85 \choose 15} \cdot 4^{70} + {85 \choose 30} \cdot 4^{55}$
(d)
${85 \choose 15} \cdot 3^{70} + {85 \choose 30} \cdot 3^{55} - {85 \choose 15} \cdot {70 \choose 30} \cdot 2^{40}$