First slide

Combinations

Question

If 20% of three subsets (i.e., subsets containing exactly three elements) of the set A = {a₁, a₂,…, a_n} contain a1, then the value of n is

Moderate

A

15
B

16
C

17
D

18

Solution

The number of subsets of A containing exactly three elements is $^{n} C_{3}$ whereas the number of three subsets of A that contain a₁ is $^{n - 1} C_{2}$ . We are given,
$\begin{array}{l} ^{n - 1} C_{2} = \frac{20}{100} (^{n} C_{3}) \\ \Rightarrow \frac{(n - 1) (n - 2)}{2} = \frac{1}{5} \frac{n (n - 1) (n - 2)}{6} \\ \Rightarrow n = 15 \end{array}$

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