1 .
Let $n \geq 2$ be an even integer. What does
$$
\sum_{k=0}^{\left. (n-2) \middle/ 2 \right.} {{n}\choose{2k+1}}
$$
count?
(a)
The number of bitstrings of length $n$.
(b)
The number of bitstrings of length $n$ having an odd number of 0's.
(c)
The number of bitstrings of length $\left. (n-2) \middle/ 2 \right.$.
(d)
The number of bitstrings of length $n$ in which the number of 0's plus the number of 1's is at most $\left. (n-1) \middle/ 2 \right.$.