Question

Evaluate P(7, 1).

1
7
5,040

Answer 1

The value of P(7, 1) is 7.

Explanation:

Given : P( 7, 1)

We have to evaluate the value of P(7, 1)

Consider the given P(7, 1)

`^nP_r` is defined as the number of the possibility of choosing an ordered set of r objects from a total of n objects.

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

Put n = 7 and r = 1 , we have,

`=(7!)/(\left(7-1\right)!)`

Simplify, we have,

`=(7!)/(\left(7-1\right)!)=7`

Thus, The value of P(7, 1) is 7.

Answer 2

The permutation formula is formulated as:


`\boxed{\text{P(n, r): } (n!)/((n - r)!)}`

`\text{P(7, 1): } (7!)/((7 - 1)!)`

`\text{P(7, 1): } (7!)/(6!) = 7`

We can further generalise this for when r = 1.
For when we are taking n objects 1 at a time, we can do this in n ways, because each permutation will be different.


`\boxed{\text{P(n, 1) = } n}`