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All the question is in the title:

How many 2-tuple can I form from the elements of a n-tuple
Supposing all elements are differents also (eg: (A,C,D,I,X,Y))

is it simply $\binom{n}{2}$ ?

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    @Shaktal $(n)_a$ is $\binom{n}{a} * a!$ like said in the ncmath's answer?2012-05-31

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If you are looking for subsets of size 2, it's $n\choose 2$. If you want ordered pairs of size 2, there are twice as many of these, so it's $n(n-1) = 2{n\choose 2}$.

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    ah right (a,b) and (b,a) is the same unordered pair2012-05-31