Respuesta :
Using the combination formula, it is found that:
a) 180 different starting lineups can be created.
b) The probability that mary and alice will get on the lineup is [tex]\frac{1}{6}[/tex].
The order in which the players are chosen is not important, hence the combination formula is used to solve this question.
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 a:
The lineup is composed by:
- 2 guards from a set of 5.
- 2 forwards from a set of 4.
- 1 center from a set of 3.
Hence the number of lineups is given by:
[tex]N = C_{5,2}C_{4,2}C_{3,1} = \frac{5!}{2!3!} \times \frac{4!}{2!2!} \times \frac{3!}{1!2!} = 180[/tex]
Item b:
The number of lineups with Mary and Alice are given as follows:
- 2 guards from a set of 5.
- Mary and 1 other forward from a set of 3.
- Alice as the center.
Hence:
[tex]n = C_{5,2}C_{3,1} = \frac{5!}{2!3!} \times \frac{3!}{1!2!} = 30[/tex]
Hence the probability is given by:
[tex]p = \frac{30}{180} = \frac{1}{6}[/tex]
The probability that mary and alice will get on the lineup is [tex]\frac{1}{6}[/tex].
More can be learned about the combination formula at https://brainly.com/question/25821700
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