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On the student government ballot at Dusable High School, the six candidates for president are listed first, followed by the four candidates for vice president, followed by the five candidates for secretary and ending with the three candidates for treasurer. In how many ways can the candidates be listed on the ballot?

 Jun 12, 2020
 #1
avatar+732 
+1

isn't it just \(6! \cdot 4! \cdot 5! \cdot 3! = 12441600‬ \text{ ways }\)?

 Jun 13, 2020
 #2
avatar+732 
+1

cause there's 6 candidates for president so that 6! 

there's 4 candidates for vp so that's 4!

there's 5 candidates for secretary so that's 5!

and there's 3 candidates for treasurer so that's 3!

 

so that's just 6!*4!*3!*5! = 12441600

lokiisnotdead  Jun 13, 2020
 #3
avatar+549 
+3

Thanks a lot!

amazingxin777  Jun 13, 2020

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