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?
+44 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 \(4!*5!*6=17280\).
+26367 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
