If ²⁴C_x = ²⁴C_{2x + 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 ⁿC_r,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.