How Many Hats Must Be Sampled to Guarantee Every Color Is Included?

[neutrino71]

In a set of 400 hats, each hat is represented by one of six colors (brown, pink, red, orange, blue, yellow). You may assume that each color is represented rather equally in the 400 hats.
What is the minimum amount of samples we must take to be likely to have a sample which has a hat of every color?

 

[mathman]

"likely" is rather qualitative. If can quantify it, say P>0.9, then an answer can be obtained, although the calculation may be a little messy.

 

[Hurkyl]

neutrino: do you have any thoughts about how you might start this problem?

 

[geosonel]

In a set of 400 hats, each hat is represented by one of six colors (brown, pink, red, orange, blue, yellow). You may assume that each color is represented rather equally in the 400 hats.
What is the minimum amount of samples we must take to be likely to have a sample which has a hat of every color?

what minimum # of hats must be drawn (without replacement) to have probability 1 of having each hat color represented at least once (if each color is "rather equally represented" in the original set of 400 hats)?
(hint: what minimum # must be drawn to use up all colors except yellow, then choose 1 more.)