contestada

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.

Respuesta :

Answer:

Combinations = 252

Permutations = 30240  

Step-by-step 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 =

[tex]^nC_r\\\\=^{10}C_5\\\\=\dfrac{10!}{5!(10-5)!}\\\\=\dfrac{10!}{5!5!}\\\\=252[/tex]

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

Possible permutations =

[tex]^nP_r\\\\=^{10}P_5\\\\=\dfrac{10!}{(10-5)!}\\\\=\dfrac{10!}{5!}\\\\=30240[/tex]

Thus, 5 tennis balls can be permuted in 30240 ways

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