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NDA Math Permutations and Combinations

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DIRECTIONS: (For the next three (03) items that follow):

Given that

C(n,r):C(n,r+1)=1:2

and

C(n,r+1):C(n,r+2)=2:3

[NDA I 2014]

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Question : 61 of 65

Marks: +1, -0

what is n equal to ?

11
12
13
14

Solution:

\frac{\binom{n}{r}}{\binom{n}{r+1}} = \frac{1}{2}

and

\frac{\binom{n}{r+1}}{\binom{n}{r+2}} = \frac{2}{3}

\Rightarrow n-3r=2

and

2n-5r=8

\Rightarrow n=14

and

r=4

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