Question

If 20% out of the subsets ( subsets containing exactly three elements) of the set $A=\{a_1,a_2,a_3.....a_n\}$ contain $a_1,$ then the value of $n$ is

• A. $15$
• B. $16$
• C. $17$
• D. $18$

Answer 1

Answer: (A)

$15$

The number of subsets of A containing exactly 3 elements is ${{}^{n}C}_3$ whereas the number of three subsets of A that contain $a_1$ is ${{}^{n-1}C}_2$. We are given,

${{}^{n-1}C}_2=\frac{20}{100}\left({{}^{n}C}_3\right)\Rightarrow \frac{(n-1)(n-2)}{2}=\frac{1}{5}\left(\frac{n(n-1)(n-2)}{6}\right)$

Thus $n=15$