If 8Cr – 7C3 = 7C2, find r.
Given:
⇒ 8Cr – 7C3 = 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.