यदि `.^(2n)C_(3): ^(n)C_(2)=12 :1` तो n का मान ज्ञात कीजिए ।

Explanation

`.^(2n)C_(3) :^(n)C_(2) = 12 :1`
` rArr ((2n)!)/(3!(2n-3)!) : (n!)/(2!(n-2)!) = 12 :1`
` rArr ((2n)*(2n-1)(2n-2))/6 : (n(n-1))/2 = 12 :1`
` rArr ((2n)(2n-1)(2n-2))/6 xx 2/(n(n-1)) = 12/1`
` rArr (2(2n-1)*2)/ 3 = 12`
` rArr 2n - 1 = 9`
` rArr n = 5`