Question: 2015 Winter Final - 2
Consider a set $S$ consisting of 20 integers; 5 of them are even and the other 15 integers in $S$
are odd. What is the number of 7-element subsets of $S$ having at least 5 even integers or at least
5 odd integers?
(a)
None of the above.
(b)
${5 \choose 5}{15 \choose 2} + {5 \choose 2}{15 \choose 5} - {5 \choose 5}{15 \choose 5}$
(c)
${5 \choose 5}{15 \choose 2} + {5 \choose 2}{15 \choose 5} + {5 \choose 1}{15 \choose 6} + {5 \choose 0}{15 \choose 7}$
(d)
${20 \choose 7} - {5 \choose 4}{15 \choose 4}$