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.