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.


4