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# Finding Different Combinations

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Imagine you've been left in charge of an ice cream stall and you have three flavours of ice cream to sell - vanilla, strawberry and chocolate.
If you're selling triples (a cone with three scoops) how many different combinations can you sell?

##### Solution Summary

Combinations are investigated and discussed in the solution.

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I am not an expert in the field of mathematics and have been given this mathematical equation to boost my problem solving skills and i have no idea on where to start.

The problem is as follows:

imagine you've been left in charge of an ice cream stall and you have three flavours of ice cream to sell - vanilla, strawberry and chocolate.
if you're selling triples (a cone with three scoops) how many different combinations can you sell.

I'm not asking for you to complete this equation for me but to offer some advise on where to start, if there is any algebraic formulae needed and how i might work this out and finally how the equation might be developed further. I've read a few maths books, but have still been left dumfounded. Many thanks in advance for your help!

Analysis.

This is a question involving combinatorial numbers. Thinking of these three types of ice cream: vanilla, strawberry and chocolate,
denoted by ...

Solution provided by:
###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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