Q. 14

# If ^{16}C_{r} = ^{16}C_{r + 2}, find ^{r}C_{4}.

Answer :

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

iii. p = q

iv. n = p + q

From the problem we can say that,

⇒ r≠r + 2

So, the condition(ii) must be satisfied,

⇒ 16 = r + r + 2

⇒ 2r = 14

⇒

⇒ r = 7.

∴ The value of r is 7.

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