Question

The number of all three element subsets of the set $\{a_1,a_2,a_3\cdots ,a_n\}$ which contain $a_3$ is:

• A. ${}^n{C}_3$
• B. ${}^{n-1}{C}_3$
• C. ${}^{n-1}{C}_2$
• D. ${}^n{C}_2$

Answer 1

The correct option is C ${}^{n-1}{C}_2$

We have to select $3$ to make subsets, since each subset must contain $a_3$, other two elements should be taken from remaining $(n-1)$ elements which can be selected in ${}^{n-1}{C}_2$ ways.