Question

For what value of n is n + 1p3 = np4

Answer 1

(n + 1) P 3 = (n + 1)(n)(n - 1)
n P 4 = n(n - 1)(n - 2)(n - 3) so make those equal. Both have n and (n - 1) so divide by those to cancel them out leaving
n + 1 = (n - 2)(n - 3)
n + 1 = n^2 - 5n + 6
0 = n^2 - 6n + 5
0 = (n - 1)(n - 5)
so n either = 1 or = 5. But it can't be 1 since the number before P has to be ≥ the number after.
So the only answer is n = 5