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Suppose we want to choose 5 colors, without replacement, from 13 distinct colors.00(a) How many ways can this be done, if the order of the choices does not matter?Х5E0(b) How many ways can this be done, if the order of the choices matters?0Submit AssignmentContinue

Suppose We Want To Choose 5 Colors Without Replacement From 13 Distinct Colors00a How Many Ways Can This Be Done If The Order Of The Choices Does Not MatterХ5E0 class=

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Question a: The correct way to get the ways 5 colors can be chosen from 13 colors is by using the combination formula since order does not matter; We have:

[tex]\begin{gathered} 13C5 \\ nCr=\frac{n!}{(n-r)!r!} \\ 13C5=\frac{13!}{(13-5)!5!} \\ \frac{13!}{8!5!}=\frac{13\times12\times11\times10\times9\times8!}{8!\times5!}=\frac{154440}{120}=1287 \end{gathered}[/tex]

Hence, the number of ways 5 colors can be chosen from 13 colors if the order does not matter is 1287 ways.

Question b: The correct way to get the ways 5 colors can be chosen from 13 colors is by using the permutation formula order does matter; We have:

[tex]\begin{gathered} 13P5 \\ nPr=\frac{n!}{(n-r)!} \\ 13P5=\frac{13!}{(13-5)!} \\ =\frac{13!}{8!} \\ =\frac{13\times12\times11\times10\times9\times8!}{8!}=154440 \end{gathered}[/tex]

Hence, the number of ways 5 colors can be chosen from 13 colors if the order matters is 154440 ways.

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