Question

if nc20 = nc4 than find the value of n.

Answer 1

nC20 = nC4
=> n! / (n-20)!20! = n! / (n-4)!4!
=> (n-20)!20! = (n-4)!4! [ after eliminating same numerator from both side and taking the reciprocal on both sides]

=> (n-20)! (20.19.18…...6.5.4!)   =  (n-4).(n-5).(n-6)…….(n-19)(n-20)! . 4!

Eliminating (n - 20)! and 4! from both sides we get:
=> (20.19.18…………6.5)   =  (n-4).(n-5).(n-6)…….(n-19)

Equating the last term from both sides, we get
5 = n – 19

Hence n = 24