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4 students from a class of 15 are going to be chosen to be on the dance committee. Findthe number of different 4-person committees that can be made.

Respuesta :

Answer:

[tex]C(15,4)=1365\text{ different committees}[/tex]

Step-by-step explanation:

This situation can be approached using the formula for combinations:

[tex]\begin{gathered} C(n,r)=\frac{n!}{r!(n-r)!} \\ \text{where,} \\ n=\text{ number of possible items that can be }selected \\ r=\text{ number of items that were selected} \end{gathered}[/tex]

Therefore, solve for n=15 and r=4.

[tex]\begin{gathered} C(15,4)=\frac{15!}{4!(15-4)!} \\ C(15,4)=1365\text{ different committees} \end{gathered}[/tex]

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