We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

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?

Guest Mar 5, 2015

#1**+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.

Melody Mar 6, 2015

#1**+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