Question

In how many ways can 7 of 10 mice can be arranged in a row for geentics experiments?

Answer 1

Number of arrangements is 604800

Explanation:

Given

`Mouse = 10` --- Total

`Mouse = 7` --- Arrangement

Required

Determine the number of ways

Since, it is an arrangement, then we make use of the following permutation formula to answer this question.

`^nP_r = (n!)/((n-r)!)`

Where

`n = 10`

`r = 7`

So:

`^nP_r = (n!)/((n-r)!)`

`^(10)P_7 = (10!)/((10-7)!)`

`^(10)P_7 = (10!)/(3!)`

`^(10)P_7 = (3628800)/(6)`

`^(10)P_7 = 604800`

Hence, number of arrangements is 604800