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Often in probability we wish to count the number of ways something can be done such as chosing a number of items from a set. This is frequently difficult to do manually as the numbers of ways can be extremely large. Because there can be various conditions on how the items are chosen, there are various techniques available to count the many ways. One such method is called combinations. where n is the number of items availble for selection and r is the number chosen. Incidentally, n! means to multiply together every integer from 1 to n. The same applies to r!. So the first step is to calculate the numerator n!. The second step is to calculate the denominator r!(nr)!. Finally, we divide the two. Now we will look at an example. Find _{5}C_{3}

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