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Combination with Restrictions

The total num...

Question

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

^{n} C_{3}

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^{n - 1} C_{3}

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^{n - 1} C_{2}

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^{n} C_{2}

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Solution

The correct option is C $^{n - 1} C_{2}$
We have to form subsets of three elements and $a_{3}$ is common to every subsets, So we need to select only 2 elements out of remaining ie $n - 1$
Required ways $=^{(n - 1)} C_{2}$

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