Question

if n!/2!(n-2)! and n!/4!(n-4)! are in the ratio 2:1 then value of n is

Answer 1

Dear student
Given n! /[2(n -2)!] : n!/[4!(n -4)!] = 2:1
=> [n! / 2! (n -2)!].[4! (n -4)! /n!] = 2/1
=> 4.3.2!.(n -4)! /[2!.(n -2).(n -3).(n -4)!] = 2/1
=> 4.3 /[(n -2)(n -3)] = 2/1
=> (n -2)(n -3) = 6
=> n² -5 n = 0      =>    n (n -5) = 0
=>   n = 0 or n = 5
But, for n = 0, (n -2)! and (n -4)! are not meaningful, therefore, n = 5.
Regards

Answer 2

Hi!

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