Q. 7

# If 15C3r = 15Cr + 3, find r.

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 nCr,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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