SOLUTION: If you have 5 types of flowers (roses, lilacs, lillys, daffodils and tulips), and your business model is to sell them prepackaged in vases. Each vase must contain 3 different type
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Question 265745: If you have 5 types of flowers (roses, lilacs, lillys, daffodils and tulips), and your business model is to sell them prepackaged in vases. Each vase must contain 3 different types of flowers (no repeats). How many combinations can you acheive?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Presuming order doesn't matter -- that is a vase with a rose, a lilac, and a lily is only one possibility regardless of whether the rose, the lilac, or the lily went into the vase first -- then you need the number of ways to select 3 things from 5 things.
The number of ways to select 
things from a collection of 
things is given by:
\ =\ \frac{n!}{r!(n\,-\,r)!})
In your case:
\ =\ \frac{5!}{3!(5\,-\,3)!}\ =\ \frac{5!}{3!2!}\ =\ \frac{5\,\cdot\,4\,\cdot\,3\,\cdot\,2\,\cdot\,1}{(3\,\cdot\,2\,\cdot\,1)(2\,\cdot\,1)})
You can do your own arithmetic.
John
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