In mathematics a combination is a way of selecting several
things out of a larger group, where (unlike permutations) order does not
matter. In smaller cases it is possible to count the number of combinations.
For example given three fruit, say an apple, orange and pear, there are three
combinations of two that can be drawn from this set: an apple and a pear; an
apple and an orange; or a pear and an orange. More formally a k-combination of a set S is a subset of k distinct elements of S. If the set has n elements the number of k-combinations is equal to the binomial coefficient
which can be
written using factorials as whenever , and which is zero when k > n. The set of all k-combinations of a set S is sometimes denoted by .(Our solved example in mathguru.com uses this concept)
Combinations
can consider the combination of n things taken k at a time without or with repetitions. In the above example
repetitions were not allowed. If however it was possible to have two of any one
kind of fruit there would be 3 more combinations: one with two apples, one with
two oranges, and one with two pears.
With large
sets, it becomes necessary to use 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 hand does not matter. There are
2,598,960 such combinations, and the chance of drawing any one hand at random
is 1 / 2,598,960.
http://en.wikipedia.org/wiki/Combination
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