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Suppose we want to choose 7 colors, without replacement, from 9 distinct colors. a) How many ways can this be done, if the order of the choices does not matter?b) How many ways can this be done, if the order if choices matter?

Answer :

b)

[tex]Npermutations=9P7=\frac{9!}{(9-7)!}=9\times8\times7\times6\times5\times4\times3=181440[/tex]

Answer: 181440 ways

a)

[tex]Ncom\text{binations=}9C7=\frac{181440}{7!}=\frac{181440}{5040}=36[/tex]

Answer: 36 ways

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