Class 11

Math

Algebra

Permutations and Combinations

Determine n if

i) $_{2n}C_{3}:_{n}C_{3}=12:1$

ii) $_{2n}C_{3}:_{n}C_{3}=11:1$

$⇒_{2n}C_{3}=12×_{n}C_{3}$

$⇒3!2n(2n−1)(2n−2) $

$=12×3!n(n−1)(n−2) $

$⇒4(2n−1)=12(n−2)$

$⇒4(2n−1)=12(n−2)$

$⇒2n−1=3(n−2)$

$⇒2n−1=3n−6$

$⇒2n−1=3n−6$

$⇒n=6−1=5$

ii) $_{2n}C_{3}:_{n}C_{3}=11:1$

$⇒_{2n}C_{3}=11×_{n}C_{3}$$⇒3!2n(2n−1)(2n−2) $

$=11×3!n(n−1)(n−2) $

$⇒4(2n−1)=11(n−2)$

$⇒4(2n−1)=11(n−2)$

$⇒8n−4=11n−22$

$⇒11n−8n=22−4$

$⇒11n−8n=22−4$

$⇒3n=18$

$⇒n=6$