Question: 2015 Winter Final - 1
Consider a set $S$ consisting of 20 integers; 5 of these are even and the other 15 integers in $S$
are odd. What is the number of 7-element subsets of $S$ having exactly 3 even integers?
(a)
${20 \choose 7}$
(b)
${5 \choose 3}{15 \choose 4}$
(c)
${5\choose 3} + {15 \choose 4}$
(d)
${5 \choose 4}{15 \choose 3}$