# Ways to place molecules

1. Aug 26, 2005

### patcho

Hi,

'How many Ways can 6 distinguishable molecules be placed in 3 different energy levels with 3 molecules in the 1st level, 2 in the 2nd level and 1 in the 3rd level, ignoring energy required?'

If it was just how many ways to place them in 3 different levels it would be easy but how to always keep 3 molecules in the first, 2 in the 2nd and 1 in the first confuses me.

I know that the number of Ways is less than before and I'm thinking along the lines of having to divide the number obtained if it was just 3 different energy levels, by 3!2!1! (the number of molecules in each level). This gives: W=10 which I think is very wrong!

Any help appreciated!

2. Aug 26, 2005

### Galileo

Take a slightly more general question:

How many ways can N numbered balls be grouped into three sets such that the first group contains $n_1$ balls, the second set $n_2$ balls and the third set $N-n_1-n_2$ balls?

Hint: How many ways are there to choose the first set? After that, in how many ways can you choose the second set?