1.

If `C(n,12)=C(n,8)` then find the values of `C(n,17)` and `C(22,n)`A. 131B. 231C. 256D. 292

Answer» Correct Answer - B
Give `C(n, 12) = C(n, 8)`
`rArr .^(n)C_(12) = .^(n)C_(8)`
`rArr (n!)/((n-12)!2!) = (n!)/((n-8)!8!)`
`rArr (1)/((n-12)!(12 xx 11 xx 10 xx 9 xx 8!))`
`= (1)/((n-8)(n-9) (n-10)(n-1)(n-12)!8!)`
`rArr (1)/(12 xx 11 xx 10 xx 9) = (1)/((n-8)(n-9)(n-10)(n-11))`
`rArr (n-8) (n-9) (n-10)(n-11)`
`= 12 xx 11 xx 10 xx 9`
`rArr n-8 = 12, n-9 = 11, n - 10 = 10 and n-11 = 9`
`rArr n = 20`
`rArr C(22, n) = .^(22)C_(20)`
`= (22!)/(2!20!) = (22 xx 21)/(2) = 231`


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