Using the combination formula, it is found that the number of possible outcomes are given by:
1. 3150
2. 700.
3. 3920.
What is the combination formula?
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Item 1:
We have combinations of 2 from 6, 5 from 7 and 3 from 5, all independent, hence we multiply them:
[tex]T = C_{6,2}C_{7,5}C_{5,3} = 15 \times 21 \times 10 = 3150[/tex]
3150 different choices are possible.
Item 2:
1 from 5, 1 from 4 and 4 from 7, hence:
[tex]T = C_{5,1}C_{4,1}C_{7,4} = 5 \times 4 \times 35 = 700[/tex]
700 different combinations are possible.
Item 3:
3 men from a set of 8, 4 women from a set of 8, hence:
[tex]T = C_{8,3}C_{8,4} = 56 \times 70 = 3920[/tex]
3920 ways to select the team of 7.
More can be learned about the combination formula at https://brainly.com/question/25821700
