#(7x圆xx5xx4xx3color(red)(xx2xx1))/color(red)(2xx1)=(7!)/(2!)#Īnd I can even go one more step and see that I can express the denominator in terms of the number of books I have and the number of books on the shelf:Īnd with this we have the general formula for a Permutation : I can now express this in terms of two factorials: I can write that as:Īnd I can sit down and multiply this out each time depending on the number of books available and the ones I intend to arrange. We could use the same sort of logic as before, see that there are 7 books we can put in the first position, 6 in the second, 5 in the third, etc, all the way to 3 at the fifth and final book. Now let's say we have 7 books and want to arrange 5 on the shelf. and so we can express the number of ways we can order the books on the shelf by saying:īecause we do this so often in Permutation and Combination problems, it'd be convenient to have some sort of symbol to let us know that we want to multiply all the natural numbers up to a given value - and this is done via the Factorial : There are 5 books we can place in the first position, 4 in the second, 3 in the third, etc. Here are the relevant bits from that answer:Ĭombinations, Permutations, and Factorials are used to help calculate the numbers of ways something can be done or ordered.įor instance, let's say we have 5 distinguishable books and want to arrange them on a shelf. I answered a question similar to this a little while ago.
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