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

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If ⁿC_{r - 1} = 36, ⁿC_r = 84 and ⁿC_{r + 1} = 126 then ?

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

Correct Option: B

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