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If nC r - 1 = 36, nC r = 84 and nC r + 1 = 126 then?

Q: If nC r - 1 = 36, nC r = 84 and nC r + 1 = 126 then?

nCr - 1 = 36, nCr = 84 and nCr + 1 = 126 ⇒ nCr / nCr - 1 = 84/36 ⇒ 3n - 10r + 3 = 0 ....(i) nCr + 1 / nCr = 126/84 ⇒ 2n - 5r - 3 = 0 .............(ii) From (i) and (ii) r = 3, n = 9

n = 8, r = 4
n = 9, r = 3
n = 7, r = 5
None of these

Correct Answer: n = 9, r = 3

Explanation:

ⁿC_{r - 1} = 36, ⁿC_r = 84 and ⁿC_{r + 1} = 126
⇒ ⁿC_r / ⁿC_{r - 1} = 84/36
⇒ 3n - 10r + 3 = 0 ....(i)
ⁿC_{r + 1} / ⁿC_r = 126/84
⇒ 2n - 5r - 3 = 0 .............(ii)
From (i) and (ii) r = 3, n = 9

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