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If .^(n)C(8) = .^(n)C(2), find .^(n)C(2)...

If `.^(n)C_(8) = .^(n)C_(2)`, find `.^(n)C_(2)`.

Text Solution

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if `""^(n)C_(x)=""^(n)C_(y)` and `x ne y` , then `x+y=n`
Now , `""^(n)C_(8)=""^(n)C_(5)`
`implies n=8+5=13`
Now, `""^(n)C_(2)=""^(13)C_(2)=(13!)/(2!(13-2)!)`
`=(13xx12xx11!)/(2!xx11!)`
=78
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