5 count bag of balloons, 6 color possibilities

[cad08cad08]

We have a standard assortment of balloons which is 6 different colors. We also have a 5 count bag of balloons which uses this standard assortment. Obviously you can get all 6 colors in a 5 count bag but my colleagues were curious about the other distributions.

The chances of only getting one color is pretty straight forward 1 out of 6^4 or 1 out of 1,296 bags will only have one color. Likewise getting 5 different colors is easy to figure out (1 * 5/6 *4/6 * 3/6 * 2/6) 120 out of 1,296 bags. My question to you is the other possibilities...2, 3, and 4 colors? Does this involve Stirling numbers?

1 color = 1/1,296
2 colors = ?
3 colors = ?
4 colors = ?
5 colors = 120/1,296

Thanks!

 

[phinds]

... Obviously you can get all 6 colors in a 5 count bag

Hm ... maybe YOU can but I don't see how.

 

[cad08cad08]

Helpful, thanks.