In how many ways can 12 different balls be divided between 2 boys, one receiving 5 and the other 7 balls? Also, in how many ways can these 12 balls be divided into groups of 5,4 and 3 balls, respectively?

Explanation

I part Here, order is important, then the number of ways in which 12 different balls can be divded between two 5 and 7 balls respectively, is

`=(12!)/(5!7!)xx2!=(12*11*10*9*8*7!)/((5*4*3*2*1)7!)*2=1584`
II part Here, order is not important, then the number of ways in which 12 different balls can be divided into three groups of 5,4 and 3 balls respectively, is
`=(12!)/(5!4!3!)=(12*11*10*9*8*7*6*5!)/(5!*4*3*2*1*3*2*1)=27720`