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There are 5 boys and 4 girls in my class. All of them are distinguishable.

In how many ways can they be seated in a row of 9 chairs such that at least 3 girls are all next to each other?

 Mar 5, 2015

Best Answer 

 #1
avatar+101741 
+5

ok

how many ways can the 3 girls sit next to each other ?   4P3 = 24

Now lets take just one of these 24 permutations and put them together with the others.

I will take the 3 girls as one (siamese triplets) + one more girl +5boys = 7  so 7! permutations.

So altogether I think that there will be   24*7! permutations

 

$${\mathtt{24}}{\mathtt{\,\times\,}}{\mathtt{7}}{!} = {\mathtt{120\,960}}$$           I think that is correct.

 

Having that 4th girl is throwing me a bit, but I think it is ok.

 Mar 6, 2015
 #1
avatar+101741 
+5
Best Answer

ok

how many ways can the 3 girls sit next to each other ?   4P3 = 24

Now lets take just one of these 24 permutations and put them together with the others.

I will take the 3 girls as one (siamese triplets) + one more girl +5boys = 7  so 7! permutations.

So altogether I think that there will be   24*7! permutations

 

$${\mathtt{24}}{\mathtt{\,\times\,}}{\mathtt{7}}{!} = {\mathtt{120\,960}}$$           I think that is correct.

 

Having that 4th girl is throwing me a bit, but I think it is ok.

Melody Mar 6, 2015
 #2
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0

that dosent work

 Feb 28, 2017

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