Answer:
There are a total of 840 possible different teams
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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
ways
The girls can be chosen in
ways
Hence;
![Total\ Selection = ^6C_4 * ^8C_5](https://tex.z-dn.net/?f=Total%5C%20Selection%20%3D%20%5E6C_4%20%2A%20%5E8C_5)
Using the combination formula;
![^nCr = \frac{n!}{(n-r)!r!}](https://tex.z-dn.net/?f=%5EnCr%20%3D%20%5Cfrac%7Bn%21%7D%7B%28n-r%29%21r%21%7D)
The expression becomes
![Total\ Selection = \frac{6!}{(6-4)!4!} * \frac{8!}{(8-5)!5!}](https://tex.z-dn.net/?f=Total%5C%20Selection%20%3D%20%5Cfrac%7B6%21%7D%7B%286-4%29%214%21%7D%20%2A%20%5Cfrac%7B8%21%7D%7B%288-5%29%215%21%7D)
![Total\ Selection = \frac{6!}{2!4!} * \frac{8!}{3!5!}](https://tex.z-dn.net/?f=Total%5C%20Selection%20%3D%20%5Cfrac%7B6%21%7D%7B2%214%21%7D%20%2A%20%5Cfrac%7B8%21%7D%7B3%215%21%7D)
![Total\ Selection = \frac{6 * 5* 4!}{2!4!} * \frac{8 * 7 * 6 * 5!}{3!5!}](https://tex.z-dn.net/?f=Total%5C%20Selection%20%3D%20%5Cfrac%7B6%20%2A%205%2A%204%21%7D%7B2%214%21%7D%20%2A%20%5Cfrac%7B8%20%2A%207%20%2A%206%20%2A%205%21%7D%7B3%215%21%7D)
![Total\ Selection = \frac{6 * 5}{2!} * \frac{8 * 7 * 6}{3!}](https://tex.z-dn.net/?f=Total%5C%20Selection%20%3D%20%5Cfrac%7B6%20%2A%205%7D%7B2%21%7D%20%2A%20%5Cfrac%7B8%20%2A%207%20%2A%206%7D%7B3%21%7D)
![Total\ Selection = \frac{6 * 5}{2*1} * \frac{8 * 7 * 6}{3*2*1}](https://tex.z-dn.net/?f=Total%5C%20Selection%20%3D%20%5Cfrac%7B6%20%2A%205%7D%7B2%2A1%7D%20%2A%20%5Cfrac%7B8%20%2A%207%20%2A%206%7D%7B3%2A2%2A1%7D)
![Total\ Selection = \frac{30}{2} * \frac{336}{6}](https://tex.z-dn.net/?f=Total%5C%20Selection%20%3D%20%5Cfrac%7B30%7D%7B2%7D%20%2A%20%5Cfrac%7B336%7D%7B6%7D)
![Total\ Selection =15 * 56](https://tex.z-dn.net/?f=Total%5C%20Selection%20%3D15%20%2A%2056)
![Total\ Selection =840](https://tex.z-dn.net/?f=Total%5C%20Selection%20%3D840)
<em>Hence, there are a total of 840 possible different teams</em>