If { }^{2 n} C_{3}:{ }^{n} C_{2}=44: 3, then the value of n is

None of the above/More than one of the above

BPSC 66th Prelims Prelims 27 Dec 2020 Solved Paper

Question : 19 of 150

Marks: +1, -0

{ }^{2 n} C_{3}:{ }^{n} C_{2}=44: 3

, then the value of

n

Solution:

{ }^{2 n} C_{3}:{ }^{n} C_{2}=44: 3

\;{\;{2 n(2 n-1)(2 n-2)}/{3 × 2 × 1}}/{{n(n-1))}/{2 × 1}}=\;{44}/{3}

\;{2 n(2 n-1)(2 n-2)}/{3(n-1)}=\;{44}/{3}

\;{4(2 n-1)(n-1)}/{3(n-1)}=\;{44}/{3}

2 n-1=11

2 n=12

{n}=6

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