Answer:
68,600
Step-by-step explanation:
The order of the players is not important. For example, a defensive line of Shaq Lawson, Ed Oliver and Jerry Hughes is the same as a defensive line of Ed Oliver, Shaq Lawson and Jerry Hughes. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Defensive Lineman:
3 from a set of 8. So
[tex]C_{8,3} = \frac{8!}{3!5!} = 56[/tex]
56 combinations of defensive lineman
Linebackers:
4 from a set of 7. So
[tex]C_{7,4} = \frac{7!}{4!3!} = 35[/tex]
35 combinations of linebackers
Defensive backs:
4 from a set of 7. So
[tex]C_{7,4} = \frac{7!}{4!3!} = 35[/tex]
35 combinations of defensive backs
How many different ways can the coach pick the 11 players to implement this particular defense?
56*35*35 = 68,600
68,600 different ways can the coach pick the 11 players to implement this particular defense
