Question

Evaluate p(7,3)
a.24
b.35
c.210

Answer 1

7P3 = 7 * 6 * 5 = 210

Answer 2

P(7,3) = 210

Explanation:

Given : P(7,3)

We have to evaluate the given permutation P(7,3)

We can define P(n,r) is defined as the number of possibilities of choosing r objects from a total of n objects.

`nPr=(n!)/(\left(n-r\right)!)`

For given P(7,3)

Put n = 7 and r = 3 , we have,

`=(7!)/(\left(7-3\right)!)`

Simplify, we have,

`=(7!)/(4!)`

Cancel the factorials,
`(n!)/(\left(n-m\right)!)=n\cdot \left(n-1\right)\cdots \left(n-m+1\right),\:n>m`

`(7!)/(4!)=7\cdot \:6\cdot \:5`

Simplify, we have,

= 210

Thus, P(7,3) = 210