how many combinations in 61 flavors

Question

how many soda combinations with 61 flavors of soda?

Answer 1

     I'm not sure if your question is worded properly or you left out some information. Questions like these usually restrict you to 2 or 3 flavors which would be 61 C 2 or 61 C 3. The way your question is worded suggests that you want ALL the combinations.....made up of 4 flavors, 5 flavors , 6 flavors , ....to all 61 flavors. That would be

61 C 0 + 61 C 1 + 61 C 2 + 61 C 3 +........+61 C 60 + 61 C 61. Luckily there is a theorem that says that instead of calculating these 62 numbers and adding them, this sum is equal to 2^61 which is a very large number.

Not sure if this will be helpful, but I hope it is.