The number of all three element subsets of the set {a1,a2,a3⋯,an} which contain a3 is:
A
nC3
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B
n−1C3
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C
n−1C2
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D
nC2
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Solution
The correct option is Cn−1C2 We have to select 3 to make subsets, since each subset must contain a3, other two elements should be taken from remaining (n−1) elements which can be selected in n−1C2 ways.