Question

Nine wolves, eight female and one male, are to be released into the wild three at a time. If the male wolf is to be in the first released group and order does not matter, in how many ways can the first group of three wolves be formed?

Answer 1

28

Explanation:

Answer 2

We have been given that Nine wolves, eight female and one male, are to be released into the wild three at a time.

We need to choose 1 male wolf out of 1 wolf male. So we can choose one wolf as:

`_(1)^(1)\textrm{C}`

`(1!)/(1!(1-1)!)`

`(1!)/(1!\cdot 0!)`

`(1)/(1\cdot 1)=1`

We can choose 1 male wolf in only 1 way.

Since the female wolfs are identical (order doesn't matter), so we will use combinations.

We can choose 2 female wolves out of 8 as:

`_(2)^(8)\textrm{C}`

`(8!)/(2!(8-2)!)`

`(8\cdot 7\cdot 6!)/(2\cdot 1\cdot 6!)=(8\cdot7)/(2)=28`

Therefore, we can choose 2 female wolves out of 8 female wolves in 28 ways.

To find number of ways in which the first group of three wolves can be formed we will multiply the ways of choosing 1 male wolf and 2 female wolves.

`\text{Number of ways of forming first group of three wolves}=1* 28=28`

Therefore, the first group of three wolves can be formed in 28 ways.