What is the meaning of "X choose Y"? [closed]

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I'm sure this is a really simple question but I hear "X choose Y" in speech. What does this mean?

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4 Answers

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"X choose Y", represented as $^X\mathrm C_Y$ or $\binom X Y$, is the count of ways to select (a subset of) $Y$ elements from a set of $X$ elements.

$$^X\mathrm C_{\lower{0.5ex}{Y}}~=~\dbinom X Y~=~\dfrac{X!}{Y!~(X-Y)!}$$

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It means the number different subsets of an $X$-element set which have size $Y$.

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If you have $X$ things, choose $Y$ of them (order isn't important).

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When you say "X choose Y," it means that you are trying to find the number of ways to select $Y$ objects for $X$ total objects. This can be written as ${X \choose Y}= \frac{X!}{Y!(X-Y)!}$

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