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