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Question: If<sup>n</sup>C<sub>6</sub> : <sup>n–3</sup>C<sub>3</sub> = 33: 4, then the value of n is...

IfnC6 : n–3C3 = 33: 4, then the value of n is

A

9

B

10

C

11

D

12

Answer

11

Explanation

Solution

nC6n−3C3\frac{nC_{6}}{n - 3C_{3}}= 334\frac{33}{4}

Ž n!/6!(n−6)!(n−3)!/3!(n−6)!\frac{n!/6!(n - 6)!}{(n - 3)!/3!(n - 6)!}= 334\frac{33}{4}

Ž n(n−1)(n−2)6.5.4\frac{n(n - 1)(n - 2)}{6.5.4}= 334\frac{33}{4}

Ž n(n – 1) (n – 2) = 30 × 33

Ž n(n – 1) (n –2) = 11 (11 –1) (11–2) Ž n = 11