Cookie problem

[dimava]

I want to see how many of you can solve this, and no this is not hw, just a math brain twister


Pat is to select six cookies from a tray containing only chocolate chip, oatmeal, and peanut butter cookies. There are at lease six of each of these kinds of cookies on the tray. How many different assortments of six cookies can be selected?

[silva]

6⁶ = 46656

s.

[sql_lall]

Umm...6⁶ isn't right cos some assortments are counted twice

Actual answer, using 'checkout principle', is 7C2

Come to think about it, this seems to small, but i'll check it.

[silva]

Are the cookies indistinguishable?

s.

[Guv]

If you expand (x+y+z)⁶ and count the terms you will get the correct answer, which I think is 27. I was not in an obsessive compulsive mood when working on this problem, so I am not sure of 27, but it should be close.

[sql_lall]

I guess we have to assume Pat can't tell the difference between cookies. Cos we are never told how many he has in total (At least 18) we can't figure out how many combinations if he could tell the difference.

However, it is interesting that the solution is quite small, cos at first, with my guess of 21, that seemed way too small, but the 27 term thing is quite close, so i guess it has to be around there somewhere