Simplify nP³\nC²+nP⁰

Answer 1

nP³ = n(n-1)(n-2)

nP⁰ = n

nP³\nC² + nP⁰ = n(n-1)(n-2)\2 + n

Simplify the above equation by expanding n(n-1)(n-2)/2:

n(n-1)(n-2)/2 = (n³ - 3n² + 2n)/2

Therefore, n(n-1)(n-2)/2 + n = (n³ - 3n² + 2n)/2 + n

Simplify the above expression further by combining like terms:

(n³ - 3n² + 2n)/2 + n = n³/2 - 3n²/2 + 2n/2 + n
= n³/2 - 3n²/2 + n/2 + n

Hence, the simplified expression is n³/2 - 3n²/2 + n/2 + n