If 24Cx = 24C2x + 3, find x.

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


i. p = q


ii. n = p + q


Let us use condition (i),


x = 2x + 3


x = – 3


We know that for a combination nCr,r≥0 and r should be an integer which is not satisfies here,


So, the condition (ii) must be satisfied,


24 = x + 2x + 3


3x = 21



x = 7.


The value of x is 7.


5