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A senate committee has 5 Republicans and 4 Democrats. In how many ways can the committee members sit in a row of 9 chairs, such that all 4 Democrats sit together?

 Jun 10, 2018
 #1
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Let us have republicans called R and Democrats called D. We can have RRRRRDDDD, RRRRDDDDR, RRRDDDDRR, RRDDDDRRR, RDDDDRRRR, and DDDDRRRRR. Notice that all cases have the same amount of arrangments. So the ways the committee members can sit is \(4!*5!*6=17280\).

 Jun 11, 2018
 #2
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A senate committee has 5 Republicans and 4 Democrats. In how many ways can the committee members sit in a row of 9 chairs, such that all 4 Democrats sit together?

 

Source:

https://www.yamathinvestigations.com/uploads/1/0/0/2/10022412/counting_and_probability.chapter_2.pdf

https://www.yamathinvestigations.com/uploads/1/0/0/2/10022412/counting.solutions.chap2.pdf

 

laugh

 Jun 11, 2018

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