Question

Lisa plays soccer 3 out of the 7 days of the week. How many possible schedules are there to play

Answer 1

Answer:

There are 25 possible schedules.

Step-by-step explanation:

The order in which they play soccer is not important(Monday and Tuesday is the same as Tuesday and Monday), and thus the combinations formula is used to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Monday but not Tuesday:

Monday(1) and 2 out of the remaining 7 - 2 = 5. So

$C_{5,2} = \frac{5!}{2!3!} = 10$

Tuesday but not Monday:

Tuesday(1) and 2 out of the remaining 7 - 2 = 5. So

$C_{5,2} = \frac{5!}{2!3!} = 10$

Monday and Tuesday:

Monday and Tuesday(1), plus one out of the remaing 5 days. So

$C_{5,1} = \frac{5!}{1!4!} = 5$

Total:

10 + 10 + 5 = 25

There are 25 possible schedules.