Question

There are 5 boys and 4 girls in my class.

In how many ways can they be seated in a row of 9 chairs such that at least 2 boys are next to each other?

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?

Answer 1

number of ways for them to sit without any restriction
= 9! = 362880
Let's calculate the number of ways for none of the boys to be together.
that can only happen this way
BGBGBGBGB
number of such ways
= 5x4x4x3x3x2x2x1 = 2880

So the number of ways with at least 2 boys together
= 362880-2880 = 360000