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

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

BITSATBITSAT 2014

Solution:

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 $^{n -1}C_2$.