# If 8Cr – 7C3 = 7C2, find r.

Given:

8Cr7C3 = 7C2

8Cr = 7C2 + 7C3

We know that nCr + nCr + 1 = n + 1Cr + 1

8Cr = 7 + 1C2 + 1

8Cr = 8C3

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),

r = 3

Let us also check condition (ii),

8 = 3 + r

r = 5

The values of ‘r’ are 3 and 5.

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