If C(n, 7) = C(n, 5), find n  Select.
A) 15 B) 12 C) 18 D) -1 E) -2
We know that C(n,r) = n! / r!(n - r)!   Now C(n,7) = C(n,5)   n! / 7! (n - 7)! = n! / 5! (n - 5)!   =&gt; 5! (n - 5)! = 7! (n - 7)!   =&gt; [5!] x [(n - 5)(n - 6)[(n - 7)!] = 7 x 6 x 5! x (n - 7)!   =&gt; n2 - 11n + 30 = 42   =&gt; n2 - 11n - 12 = 0   =&gt; (n - 12)(n + 1) = 0   =&gt; n = 12 or n = - 1   But n = - 1 is rejected as n is a non negative integer. Therefore, n = 12   ANSWER:12
<result>B</result>
If C(n, 7) = C(n, 5), find n