If one quarter of all three element subsete of the set `A={a_(1),a_(2),a_(3),......,a_(n)}` contains the element `a_(3)`, then n=

Options

A. 10
B. 12
C. 14
D. none of these

Explanation

There are `""^(n)C_(3)` three element subsets of set A, and `""^(n-1)C_(2)` three element subsets containing `a_(3)`.
`:.(1)/(4)(""^(n)C_(3))=""^(n-1)C_(2)`
`implies(n(n-1)(n-2))/(24)=((n-1)(n-2))/(2)impliesn=12`