1 .
Let $n \geq 4$ be an even integer and let $k$ be an integer with $1 \leq k \leq n/2$. Consider
strings consisting of $n$ characters, such that
- each character is an element of $\{a, b, c\}$,
- the number of $a$'s is equal to $k$, and
- each $a$ is at an even position.
(a)
${n \choose k} cdot 2^{n-k}$
(b)
${n \choose k} \cdot 2^{n/2}$
(c)
${n/2 \choose k} \cdot 2^{n/2}$
(d)
${n/2 \choose k} \cdot 2^{n-k}$