Yogurt flavors

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azpilot2008

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Oct 9, 2014
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Hello and thank you for taking a look at my math problem.

I am the operations manager for a self-serve yogurt company and I am trying to figure out how many different combinations of flavors could a customer have? We have 16 different yogurt flavors at all times. I have tried 16! and came up with almost 21 trillion combinations but i know this can not be accurate; someone having the combination of vanilla and chocolate is the same as someone having chocolate and vanilla, so that combination should only be counted once, not twice. Obviously the number of combinations will be less when restrictions are put on it such as: a customer can only choose two flavors, or three flavors.

How many total flavor combinations are there, all possibilities with 16 flavors?
How many different combinations if a person can only choose two flavors at a time?

Thank you for taking the time to read this and help me out, it is much appreciated and I am hoping to use the answer as a advertisement piece or maybe a trivia question for someone to win free yogurt.
 
azpilot2008 said:
Hello and thank you for taking a look at my math problem.

I am the operations manager for a self-serve yogurt company and I am trying to figure out how many different combinations of flavors could a customer have? We have 16 different yogurt flavors at all times. I have tried 16! and came up with almost 21 trillion combinations but i know this can not be accurate; someone having the combination of vanilla and chocolate is the same as someone having chocolate and vanilla, so that combination should only be counted once, not twice. Obviously the number of combinations will be less when restrictions are put on it such as: a customer can only choose two flavors, or three flavors.

How many total flavor combinations are there, all possibilities with 16 flavors?
How many different combinations if a person can only choose two flavors at a time?

Thank you for taking the time to read this and help me out, it is much appreciated and I am hoping to use the answer as a advertisement piece or maybe a trivia question for someone to win free yogurt.
Click to expand...

Some notation: \(\displaystyle \dbinom{N}{k}=\dfrac{N!}{k!(N-k)!}\)

So \(\displaystyle \dbinom{16}{2}=\dfrac{16!}{2!(14!)!}=120\) if a person can choose two flavors.

It is 560 if a person can choose three flavors.

It is 12870 if a person can choose eight flavors, that is the most possible.
 
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