Question: 2018 Fall Final - 3
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 $c$ or exactly 30 letters $b$?
(a)
None of the above.
(b)
${70 \choose 12} \cdot 2^{58} + {70 \choose 30} \cdot 2^{40}$
(c)
${70 \choose 12} + {70 \choose 30} - {58 \choose 30}$
(d)
${70 \choose 12} \cdot 2^{58} + {70 \choose 30} \cdot 2^{40} - {70 \choose 12} \cdot {58 \choose 30}$