Answer :

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),

⇒ 3r = r + 3

⇒ 2r = 3

⇒

⇒

⇒

We know that for a combination ^{n}C_{r},r≥0 and r should be an integer, which is not satisfies here,

So, the condition (ii) must be satisfied,

⇒ 15 = 3r + r + 3

⇒ 4r = 12

⇒

⇒ r = 4.

∴ The value of r is 4.

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Prove that the product of 2n consecutive negative integers is divisible by (2n)!

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Fill in the Blanks

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