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Pascal's Triangle

Part of 'Pascal's triangle' is shown below. In any row, each number is calculated by adding the two numbers above it, so you can readily calculate subsequent rows of the triangle. For clarity, we have omitted the zeros.

The constants for 0 to n successes, where n is the sample size.

Again from Pascal's triangle, the column of totals to the right indicate the total number of combinations available at that sample size. Arithmetically, this is equal to 2n. For samples of more than 10 observations, the coefficients can be calculated as n!/(y![n!-y!]) where x and n have the same values as above, but are evaluated as their factorials.