If n C 10 = n C 12 , find 23 C n .

Question

Philoid · Accepted Answer

We know that if , then one of the following conditions need to be satisfied:

i. p = q

ii. n = p + q

From the problem we can say that,

⇒ 10≠12

So, the condition(ii) must be satisfied,

⇒ n = 10 + 12

⇒ n = 22.

We need to find the value of

We know that ..... (1)

And also n! = n(n – 1)(n – 2)…………2.1

From (1)

⇒

∴ The value of is 23.

If nC10 = nC12, find 23Cn.