Question

a company has 12 male and 7 female employees, and needs to nominate 3 men and 3 women for the company bowling team. how many different teams can be formed?

Explanation:

Step1: Calculate number of ways to choose 3 men

Use combination formula $C(n,k)=\frac{n!}{k!(n - k)!}$, where $n = 12$ (number of men) and $k=3$. So $C(12,3)=\frac{12!}{3!(12 - 3)!}=\frac{12\times11\times10}{3\times2\times1}=220$.

Step2: Calculate number of ways to choose 3 women

Use combination formula with $n = 7$ (number of women) and $k = 3$. So $C(7,3)=\frac{7!}{3!(7 - 3)!}=\frac{7\times6\times5}{3\times2\times1}=35$.

Step3: Calculate total number of teams

By multiplication - principle, multiply the number of ways to choose men and women. Total number of teams is $C(12,3)\times C(7,3)=220\times35 = 7700$.

Answer:

7700