The number of all three elements subsets of the set a1, a2, a3 . . . an which contain a3 is

Question

The number of all three elements subsets of the set a1, a2, a3 . . . an which contain a3 is (A) nC3 (B) n - 1 C3 (C) n - 1 C2 (D) None of these

Tardigrade Admin · Accepted Answer

The number of three elements subsets containing a3 is equal to the number of ways of selecting 2 elements out of n - 1 elements. So, the required number of subsets is n -1C2.

Q. The number of all three elements subsets of the set ${a_{1}, a_{2}, a_{3} ... a_{n}}$ which contain $a_{3}$ is

$^{n} C_{3}$

$^{n - 1} C_{3}$

$^{n - 1} C_{2}$

None of these

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 $^{n - 1} C_{2}$ .

Q. The number of all three elements subsets of the set {a1​,a2​,a3​...an​} which contain a3​ is

nC3​

n−1C3​

n−1C2​