Question

Suppose there are 10 tennis balls in a basket each of a different color. Find the numbers of waysin which you can combine and permute the tennis balls if you select five tennis balls at a time.

Answer 1

Combinations = 252

Permutations = 30240

Explanation:

We are given the following in the question:

Total number of tennis balls = 10

Number of tennis balls to be selected = 5

Possible combinations =

`^nC_r\\\\=^(10)C_5\\\\=(10!)/(5!(10-5)!)\\\\=(10!)/(5!5!)\\\\=252`

Thus, 5 tennis balls can be combined in 252 combinations.

Possible permutations =

`^nP_r\\\\=^(10)P_5\\\\=(10!)/((10-5)!)\\\\=(10!)/(5!)\\\\=30240`

Thus, 5 tennis balls can be permuted in 30240 ways