Question

I have two questions......1. Leslie has 7 books. There is enough space on a shelf for 3 books. In how many ways can 3 of the 7 books be arranged on the shelf?

2. Out of the 12 girls who tried out for the softball team, 10 will be chosen for the team. Find the number of different 10-person teams.

Answer 1

These are both combination questions which is written as C(n,r), where n is the number of objects and r is the number of the sample.

1. 7 total books, 3 on the shelf:
n = 7, r = 3

The formula would be: 7! / (3!(7-3)!)
= 7*6*5*4*3*2 / (3*2(4*3*2)
=5040 / (6*24)
= 5040 / 144
= 35 different ways.

2. n = 12, r = 10
12! / (10!(12-10)!)
= 66 different ways.