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 Amsco Integrated Algebra I: Combinations
This is a free lesson from our course in Amsco's Integrated Algebra
This lesson explains combination.A combination is a collection of things in which order is not important. A combination is an arrangement of objects, without repetition, and in which order is not important. In general, for counting numbers n and r, where r ≤ n, the number of combinations of n things taken r at a time is found by using the formula: nCr=nPr/r! .E.g. Let us take a look at how many 5 card poker hand are there with 3 clubs and 2 diamonds? You know that there are 13 clubs and we want 3 of them, so there are C(13,3) = 286 ways to get them. Then there are 13 diamonds and we want 2 of them, there are C(13,2) = 78 ways to get them.  (More text below video...)
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(Continued from above) As we want them both to occur at the same time, use the fundamental counting principle and multiply 286 and 78 together which results in 22,308 possible hands.
Take an example: the combination of 4 things taken 2 at a time is 4C2=4P2/2!=(4*3)/(1*2)=6. Some points to be remembered are: The distinguishing feature between Permutations and Combinations is whether or not order is important.


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