10th July Learning essay of probability

A A A B B C

How many different orderings of these above six letters ?

1. Choose 3 from 6 for three As

2.Choose 2 from 3 for two Bs

or 

Choose 2 from 6 for two Bs

Choose 3 from 4 for three As

or 

Assume that there are totally different 6 letters, so there are 6 x 5 x 4 x 3 x 2 x 1 == 720

Then because there are 3 repeated As and 2 duplicate Bs, so you have to divide them

720/3!2! = 60

A student 

Choose n people from N to be committees, then you need to choose one of them to be president,

B student

You firstly choose one people from N to be the president, then you n-1 from N-1 to be members of committees.