1 .
Let $n \geq 7$ and $k \geq 1$ be integers, let $A$ be the set of all bitstrings of length $n$ that
contain exactly seven 0s, and let $B$ be the set of all bitstrings of length $k$ that contain at
least one 1. Assume there exists a one-to-one function $f : A \rightarrow B$. Which of the following
is true?
(a)
$2^k - 1 \geq {n \choose 7}$
(b)
$2^k - 1 < {n \choose 7}$
(c)
$2^k - 1 < \left. 2^n \middle/ {n \choose n-7} \right.$
(d)
$2^k - 1 \geq \left. 2^n \middle/ {n \choose n-7} \right.$