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Sagot :
Explanation
The number of different teams that can be formed is given by the product of two numbers:
1. The number of different ways that 2 male employees can be selected.
2. The number of different ways that 2 female employees can be selected.
The first number is given by all the possible ways to select 2 males out of 9 without caring about the order. This last part basically means that even though there are two ways to select two particular males (let's name them A and B), which are AB and BA, they count as a single way. This implies that what we are looking for is the total number of combinations. In general, the total number of combinations when selecting k items from a total of n is given by:
[tex]_nC_k=\frac{n!}{(n-k)!k!}[/tex]Then the number of different ways that 2 male employees can be selected is given by:
[tex]_9C_2=\frac{9!}{(9-2)!2!}=\frac{9!}{7!2!}=36[/tex]For the number of different ways that 2 female employees can be selected we can do the same. The only difference is that here we have a total of 7 people to select from:
[tex]_7C_2=\frac{7!}{(7-2!)2!}=\frac{7!}{5!2!}=21[/tex]Then the number of different teams that can be formed is given by the product of the two numbers that we found:
[tex]N=36\cdot21=756[/tex]AnswerThen the answer is 756.
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