At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
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.
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
