Question 265745
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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 *[tex \Large r] things from a collection of *[tex \Large n] things is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(n\cr r\right)\ =\ \frac{n!}{r!(n\,-\,r)!}]


In your case:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(5\cr 3\right)\ =\ \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
*[tex \LARGE e^{i\pi} + 1 = 0]
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