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The number of all three element subsets ...

The number of all three element subsets of the set `{a_(1),a_(2),a_(3)......a_(n)}` which contain `a_(3)` , is

A

`""^(n)C_(3)`

B

`""^(n-1)C_(3)`

C

`""^(n-1)C_(2)`

D

none of these

Text Solution

Verified by Experts

The number of three element subsets contaning `a^(3)` is equal to the number ways of selecting 2 elements out of n-1 elements.
So, the required number of subsets `=""^(n-1)C_(2)`.
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Knowledge Check

  • The number of subsets of the set A={a_(1),a_(2), . . .,a_(n)} which contain even number of elements is

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    15
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