More probability/counting

[Random Variable]

Let's say there are 3 mugs of beer :beer::beer::beer:, 4 glasses of wine :wine::wine::wine::wine:, 4 cameras :camera::camera::camera::camera:, 5 red roses

, and 3 clocks :clock::clock::clock:.

And let's say you want to select five of these items and the order does not matter (e.g., :beer::beer::beer::wine:

= :beer::wine::beer:

:beer: ).

How many ways can this be done? I don't know if a method exists to solve the problem without actually listing all the possible combinations.

 

[Zugzwang152]

3*4*4*5*3 - (insert formula to find number of like sets)?

 

[Random Variable]

Originally posted by: Zugzwang152
3*4*4*5*3 - (insert formula to find number of like sets)?

I think it's more like 9C5 (the number of possible combinations if there were at least 5 of each item) - the combination that has 5 mugs of beer - the combination that has 5 glasses of wine - the combination that has 5 cameras - the combination that has 5 clocks- the combinations that have 4 mugs of beer - the combinations that have 4 clocks = 126-1-1-1-1-4-4 = 114.

The problem would have been even harder if there were like only 2 mugs of beer and only one clock.