1 .
Consider strings consisting of 40 characters, where each character is an element of $\{a,b,c,d\}$.
How many such strings contain exactly five $a$'s or exactly five $c$'s?
(a)
$2 \cdot {40 \choose 5} - {40 \choose 5} \cdot {35 \choose 5}$
(b)
${40 \choose 5} + {35 \choose 5} - {40 \choose 5} \cdot {35 \choose 5}$
(c)
$2 \cdot {40 \choose 5} \cdot 3^{35}$
(d)
$2 \cdot {40 \choose 5} \cdot 3^{35} - {40 \choose 5} \cdot {35 \choose 5} \cdot 2^{30}$