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The Senate in a certain state is comprised of 6060 ​Republicans, 3838 ​Democrats, and 22 IndependentsIndependents. How many committees can be formed if each committee must have 33 Republicans and 22 ​Democrats?

Respuesta :

Answer:

There can be 24056660 committees.

Step-by-step explanation:

The Senate in a certain state is comprised of 60 ​Republicans, 38 ​Democrats, and 22 Independents.

Number of ways to pick 3 Republicans : 60C3 = [tex]\frac{60!}{3!(60-3)!}[/tex] = 34220

Number of ways to pick 2 ​Democrats : 38C2 = [tex]\frac{38!}{2!(38-2)!}[/tex]

= 703

And total number of committees formed = [tex]34220\times703=24056660[/tex]

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