Two boys and three girls are going to sit around a table with 5 different chairs. If the two boys want to sit together, in how many possible ways can they be seated?
Assuming that all rotations of the same seating pattern are the same....we can seat the boys next to each other.....and this can ve done in two ways....then.....the three girls can be seated in 3! = 6 ways
So... 2 ways * 6 ways = 12 different ways
So we can approach the problem by solving with "blocks".
WE put the boys in a single "block" and assume tht they are a single person.
Now there are four people since the boys are a block
We can do 4! 4*3*2*1 = 24 to find out how many ways to seat them all. But the boys can also switch in between themselves, so we get 24*2 = 48
We forgot rotational symmetry though so we have to divide by 4 (the number of people there are) since moving them around a table is considered the same rotation.
And then you get your final equation (4!*2!)/4
*The problem should be labled Combination not Permutation