Question

A team of four boys and five girls is to be chosen from a group of six boys and eight girls. How many different teams are possible?​

Answer 1

Answer:

There are a total of 840 possible different teams

Step-by-step explanation:

Given

Number of boys = 6

Number of girls = 8

Required

How many ways can 4 boys and 5 girls be chosen

The keyword in the question is chosen;

This implies that, we're dealing with combination

And since there's no condition attached to the selection;

The boys can be chosen in $^6C_4$ ways

The girls can be chosen in $^8C_5$ ways

Hence;

$Total\ Selection = ^6C_4 * ^8C_5$

Using the combination formula;

$^nCr = \frac{n!}{(n-r)!r!}$

The expression becomes

$Total\ Selection = \frac{6!}{(6-4)!4!} * \frac{8!}{(8-5)!5!}$

$Total\ Selection = \frac{6!}{2!4!} * \frac{8!}{3!5!}$

$Total\ Selection = \frac{6 * 5* 4!}{2!4!} * \frac{8 * 7 * 6 * 5!}{3!5!}$

$Total\ Selection = \frac{6 * 5}{2!} * \frac{8 * 7 * 6}{3!}$

$Total\ Selection = \frac{6 * 5}{2*1} * \frac{8 * 7 * 6}{3*2*1}$

$Total\ Selection = \frac{30}{2} * \frac{336}{6}$

$Total\ Selection =15 * 56$

$Total\ Selection =840$

Hence, there are a total of 840 possible different teams