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Anissa is creating a poster for a school assignment. She has 10 different colored markers to choose from and hasdecided to use 4 colors to create the poster. In how many ways can she select the 4 colors for the poster?

Sagot :

Anissa has 10 different colored markers and she wants to use 4 colors to create the poster. Therefore, in order to see how many ways she can select the 4 colors, we must use the combination formula:

[tex]\begin{gathered} \frac{n!}{r!(n!-r!)}=^nC_r \\ \\ n!=\text{ 10} \\ r!=4 \\ \\ \frac{10!}{4!(10!\text{ -4!\rparen}}= \\ \frac{(10!)(9!)(8!)(7!)(6!)}{4!\text{ \lparen6!\rparen}}=\text{ we eliminate 6!}which\text{ is repeated in both numerator and denominator} \\ \\ \frac{(10!)(9!)(8!)(7!)}{(4!)(3!)(2!)(1!)}= \\ \\ \frac{5,040}{24}= \\ \\ 210 \end{gathered}[/tex]

Therefore, there are 210 possible ways she can select 4 colors for the poter.

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