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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?

paullb
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    Have you done any research on your own for this? When I google the part of your question in quotes, the first hit is the Wikipedia page answering this, and the third hit is a Quora question answering your exact question. –  Aug 31 '16 at 23:59
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    @T.Bongers I checked but was unable to confirm. Quora question does come up first but it is not the same text. Wikipeida article that comes up third appears to be binomial coefficient which is something else, no? Not everybody has the same level of knowledge as you. – paullb Sep 02 '16 at 00:36

4 Answers4

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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.

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

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

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

Sean Lake
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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 ${X \choose Y}= \frac{X!}{Y!(X-Y)!}$

clache547
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