Question

Simplify nP3/nP2+nP0​

Option 1: n - 3
Option 2: n^3 - n
Option 3: n^2 - 1
Option 4: n + 3

Answer 1

To simplify the expression nP3/nP2+nP0, we can start by simplifying the individual terms. nP3 represents the number of permutations of n objects taken 3 at a time, nP2 represents the number of permutations of n objects taken 2 at a time, and nP0 represents the number of permutations of n objects taken 0 at a time (which is always 1). Therefore, nP3/nP2+nP0 simplifies to n-1.

Step-by-step explanation:

To simplify the expression nP3/nP2+nP0, we can start by simplifying the individual terms. nP3 represents the number of permutations of n objects taken 3 at a time, nP2 represents the number of permutations of n objects taken 2 at a time, and nP0 represents the number of permutations of n objects taken 0 at a time (which is always 1).

Therefore, nP3/nP2+nP0 simplifies to n(n-1)(n-2)/n(n-1) + 1. Cancelling out common factors, we get (n-2) + 1, which simplifies to n-1.

So the simplified expression is n-1.