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search    \binom nk = \frac{n(n-1)\ldots(n-k+1)}{k(k-1)\dots1},
which can be written using factorials as \frac{n!}{k!(n-k)!}
whenever k\leq n, and which is zero when k>n. The set of all
k-combinations of a set S is sometimes denoted by \binom Sk\,.
Combinations refer to the combination of n things taken k at a
time without repetition. To refer to combinations in which
repetition is allowed, the terms k-selection,[1] k-multiset,[2]
or k-combination with repetition are often used.[3] If, in the
above example, it was possible to have two of any one kind of
fruit there would be 3 more 2-selections: one with two apples,
one with two oranges, and one with two pears.  With large sets,
it becomes necessary to use more sophisticated mathematics to
find the number of combinations. For example, a poker hand can
be described as a 5-combination (k = 5) of cards from a 52 card
deck (n = 52). The 5 cards of the hand are all distinct, and the
order of cards in the