Question

The sport of korfball is played by teams of eight players. Each team has fourmen and four women on it. Halliday High School has seven men and 11 women interested in playing korfball.In how many ways can they form a korfball team from their 18 interested students

Answer 1

To form a korfball team from the students at Halliday High School, the number of ways they can form the team is 11,550.

Step-by-step explanation:

To form a korfball team from the interested students at Halliday High School, we need to select 8 players from a group of 7 men and 11 women. The selection must include 4 men and 4 women. We can solve this problem using combinations.

The number of ways to select 4 men from a group of 7 is denoted as C(7,4) and can be calculated as:

C(7,4) = 7! / (4!(7-4)!) = (7*6*5*4) / (4*3*2*1) = 35

The number of ways to select 4 women from a group of 11 is denoted as C(11,4) and can be calculated as:

C(11,4) = 11! / (4!(11-4)!) = (11*10*9*8) / (4*3*2*1) = 330

Since the selection of men and women is independent, we can multiply the two combinations to get the total number of ways to form the korfball team:

Total ways = C(7,4) * C(11,4) = 35 * 330 = 11,550

Answer 2

There are 11550 possible selections

Step-by-step explanation:

Given

`Men = 7`

`Women = 11`

Required

How many ways can 4 men and 4 women be selected

The keyword in the question is SELECTION and it means COMBINATION;

So, number of selection is:

`Number = Men * Women`

`Number = ^7C_4 * ^(11)C_4`

This gives

`Number = (7!)/((7-4)!4!) * (11!)/((11-4)!4!)`

`Number = (7!)/(3!4!) * (11!)/(7!4!)`

`Number = (7 * 6 * 5 * 4!)/(3!4!) * (11 * 10 * 9 * 8 * 7!)/(7!4!)`

`Number = (7 * 6 * 5)/(3!) * (11 * 10 * 9 * 8)/(4!)`

`Number = (7 * 6 * 5)/(3 * 2 * 1) * (11 * 10 * 9 * 8)/(4 * 3 * 2 * 1)`

`Number = (7 * 6 * 5)/(6) * (11 * 10 * 9 * 8)/(4 * 3 * 2 * 1)`

`Number = 7 * 5 * (11 * 10 * 9 * 8)/(4 * 3 * 2 * 1)`

`Number = 7 * 5 * (7920)/(24)`

`Number = 7 * 5 * 330`

`Number = 11550`

Hence;

There are 11550 possible selections