How to Calculate Combinations of Two Groups of Numbers
- 1). Establish how many numbers, or elements, there are in each group. The values of the individual numbers is not important, just the total number of elements in each group.
For example, if a group contains 1, 7, 3 and 22, there are four elements in the group. Add the totals for both groups to establish the overall number of elements. This value is known as "n." - 2). Determine "r," the size of the combinations. For example, any number of elements combined into groups of three has an "r" value of three.
- 3). A factorial of a number is the value of the number multiplied by every whole number smaller than itself down to one, so 4! is the same as 4x3x2x1. The "!" sign means factorial.
Substitute the values for "n" and "r" into the formula: C = n! / r!(n-r)! where C stands for the number of possible combinations. For example, with n = 10 and r = 3, the formula becomes C = 10! / 3!(10-3)! - 4). Use the factorial button on a calculator, or long multiplication, to determine the value of each factorial in the equation. Using the example above C = 3628800 / 6 x 5040. The result, in this example 120, is the number of possible combinations of two groups of "n" numbers, in sets of size "r."
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