If nC10 = nC12, find 23Cn.
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.