Question

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

• A. $^nC_3$
• B. $^{n - 1} C_3$
• C. $^{n - 1} C_2$
• D. None of these

Answer 1

Answer: (C)

$^{n - 1} C_2$

Answer 2

The number of three elements subsets containing $a^3$ is equal to the number of ways of selecting $2$ elements out of $n - 1$ elements. So, the required number of subsets is $^{n -1}C_2$.