Question: 2017 Winter Midterm - 4
Let $n \geq 13$ be an integer. What is the number of bitstrings of length $n$ that have exactly
seven 0's or exactly five 1's?
(a)
${n \choose 12} \cdot {12 \choose 7}$
(b)
${n \choose 7} + {n \choose 5} - {n \choose 5} \cdot {n - 5 \choose 7}$
(c)
None of the above.
(d)
${n \choose 7} + {n \choose 5}$