Answer:
[tex]Total\ Selection = 30\ ways[/tex]
Step-by-step explanation:
Given
Girls = 3
Boys = 5
Required
How many ways can 2 boys and girls be chosen?
The keyword in the question is chosen;
This implies combination and will be calculated as thus;
[tex]Selection =\ ^nC_r = \frac{n!}{(n-r)!r!}[/tex]
For Boys;
n = 5 and r = 2
[tex]Selection =\ ^5C_2[/tex]
[tex]Selection = \frac{5!}{(5-2)!2!}[/tex]
[tex]Selection = \frac{5!}{3!2!}[/tex]
[tex]Selection = \frac{5 * 4 * 3!}{3!*2 * 1}[/tex]
[tex]Selection = \frac{20}{2}[/tex]
[tex]Selection = 10[/tex]
For Girls;
n = 3 and r = 2
[tex]Selection =\ ^3C_2[/tex]
[tex]Selection = \frac{3!}{(3-2)!2!}[/tex]
[tex]Selection = \frac{3!}{1!2!}[/tex]
[tex]Selection = \frac{3 * 2!}{1 *2!}[/tex]
[tex]Selection = \frac{3}{1}[/tex]
[tex]Selection = 3[/tex]
Total Selection is calculated as thus;
[tex]Total\ Selection = Boys\ Selection * Girls\ Selection[/tex]
[tex]Total\ Selection = 10 * 3[/tex]
[tex]Total\ Selection = 30\ ways[/tex]