Question #5cc63

1 Answer
Jun 12, 2017

Ahhh, we can used permuatations:

Explanation:

Let's use factorials, firstly:

#!# (These things)

So, to find all the possible combinations, we know that there are, in total, #12# variables, #b1 , b2, b3# etc.

So, the amount of total possible arrangements are:

#12!#

= #479001600#

That's a pretty big number...

Now, out of these combinations, we know that there are:

#6!# ways that the girls can sit together...

= #720#

Therefore, we can now find the amount of ways that the girls can sit together, and the amount of ways the girls sit together, respectively:

Ways (Boys/Girls) = #479001600 - 720# = #479000880#

Ways (Girls) = #720#

Therefore, the probability that the girls sit together is:

#479001600/720#

And the probability that the boys and girls sit together in a seperate combination is:

#479000880/479001600#

What? You said #g1 = g6#?!

That's for another time, my young friend...