For instance, imagine that you're going to order 5 items from a menu offering 15 items the order of your selections doesn't matter, and you don't mind getting multiples of the same item (i.e., repetitions are allowed).In this kind of problem, you can use the same item more than once. This means that there are 210 different ways to combine the books on a shelf, without repetition and where order doesn't matter.Ĭonsider an example problem where order does not matter but repetition is allowed. In the example case, you'd do get 210.Divide the factorial of the total by the denominator, as described above: 3,628,800/17,280.In this example, you should have 24 * 720, so 17,280 will be your denominator. Then multiply the two numbers that add to the total of items together.Find 4! with (4 * 3 * 2 * 1), which gives you 24. If you have to solve by hand, keep in mind that for each factorial, you start with the main number given and then multiply it by the next smallest number, and so on until you get down to 0.If you're using Google Calculator, click on the x! button each time after entering the necessary digits. If you have a calculator available, find the factorial setting and use that to calculate the number of combinations. You can do this either by hand or with a calculator. Solve the equation to find the number of combinations.
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