Q. 84.5( 6 Votes )

If 8Cr7C3 = 7C2, find r.

Answer :

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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