Question: 2018 Fall Midterm - 7
Consider 5-element subsets $\{x_1,x_2,x_3,x_4,x_5\}$ of the set $\{1,2,3,\dots,17\}$,
where $x_1 < x_2 < x_3 < x_4 < x_5$.
How many such subsets have the property that $x_3 = 7$?
How many such subsets have the property that $x_3 = 7$?
(a)
${7 choose 2} cdot {9 choose 2}$
(b)
${6 choose 2} cdot {10 choose 2}$
(c)
${7 choose 2} cdot {10 choose 2}$
(d)
${6 choose 2} cdot {9 choose 2}$