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

Question

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Respuesta :

MrRoyal MrRoyal · Answer 1 · 2020-09-20T02:49:22+02:00

Answer:

There are 11550 possible selections

Step-by-step explanation:

Given

[tex]Men = 7[/tex]

[tex]Women = 11[/tex]

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:

[tex]Number = Men * Women[/tex]

[tex]Number = ^7C_4 * ^{11}C_4[/tex]

This gives

[tex]Number = \frac{7!}{(7-4)!4!} * \frac{11!}{(11-4)!4!}[/tex]

[tex]Number = \frac{7!}{3!4!} * \frac{11!}{7!4!}[/tex]

[tex]Number = \frac{7 * 6 * 5 * 4!}{3!4!} * \frac{11 * 10 * 9 * 8 * 7!}{7!4!}[/tex]

[tex]Number = \frac{7 * 6 * 5}{3!} * \frac{11 * 10 * 9 * 8}{4!}[/tex]

[tex]Number = \frac{7 * 6 * 5}{3 * 2 * 1} * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]

[tex]Number = \frac{7 * 6 * 5}{6} * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]

[tex]Number = 7 * 5 * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]

[tex]Number = 7 * 5 * \frac{7920}{24}[/tex]

[tex]Number = 7 * 5 * 330[/tex]

[tex]Number = 11550[/tex]

Hence;

There are 11550 possible selections