Question

Find the value of n such that :

nP4 / n-1P4 = 5/3 , n>4
from permutation and combination chapter

Answer 1

np4 = n!/(n-4)! = n(n-1)(n-1)(n-3)

n-1p4 = (n-1)(n-2)(n-3)(n-4)

Now np4/n-1p4 = 5/3 i.e

3(n)(n-1)(n-2)(n-3) = 5(n-1)(n-2)(n-3)(n-4)

By removing (n-1)(n-2)(n-3) i.e

3n=5n-20

20 = 2n

n = 10.

Hope this helps:)