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Q9 of 68 Page 330

If ⁿC_r–1 = 36, ⁿC_r = 84 and ⁿC_r+1 = 126, find r.

Given, ⁿC_r–1 = 36, ⁿC_r = 84 and ⁿC_r+1 = 126

To find:r=?

⇒

⇒

⇒

⇒3(n-r+1)=7r

⇒3n-10r=-3….(1)

⇒

⇒

⇒

⇒2(n-r)=3(r+1)

⇒2n-5r=3….(2)

From equations 1 & 2 we get

n=9 & r=3

Ans:r=3

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