permutations and combination

Question

If np3/nc4 =6, find the value of n

Answer 1

_nP₃ = n! / (n - 3)!

_nC₄ = n! / 4!(n - 4)!

 

[ n! / (n - 3)! ] / [ n! / 4!(n - 4)! ] = 6

4!(n - 4)! = 6(n - 3)!

24(n - 4)! = 6(n - 3)!

4(n - 4)! = (n - 3)!

4(n - 4)! = (n - 3)(n - 4)!

4 = n - 3

7 = n