Question

can anyone help me with this ??

Answer 1

A. 336

B. Arranging 3 people in 8 chairs.

C. 42

B. Arranging 2 people in 7 chairs.

Explanation:

A.

`P(n, r) = P(8, 3)`

Formula for Permutation is given as:

`P(n, r) = (n!)/((n-r)!)`

Putting the value of
`n` = 8 and
`r =3` , we get:

`P(8, 3) = (8!)/((8-3)!) \\\Rightarrow (8* 7 * 6 * 5* 4 * 3 * 2* 1)/(5* 4 * 3* 2* 1)\\\Rightarrow 8* 7 * 6 \\\Rightarrow 336`

B. Real world situation for part A:

Arranging 3 people on 8 chairs.

First person has 8 options.

Second person has 7 options.

Third person has 6 options.

C.

`P(n, r) = P(7, 2)`

Formula for Permutation is given as:

`P(n, r) = (n!)/((n-r)!)`

Putting the value of
`n` = 7 and
`r` = 2 , we get:

`P(7, 2) = (7!)/((7-2)!) \\\Rightarrow (7 * 6 * 5* 4 * 3 * 2* 1)/(5* 4 * 3* 2* 1)\\\Rightarrow 7 * 6 \\\Rightarrow 42`

D. Real world situation for part AC:

Arranging 2 people on 7 chairs.

First person has 7 options.

Second person has 6 options.