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Functions for partial factorials, factorials, binomial coeffs., & rows...

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The factorial of 5 is:
[1] 120
[1] 20

The number of ways to combine 6 things taken 3 at a time: 20

Rows 2-7 of Pascale's Triangle: 
[1] 1 2 1
[1] 1 3 3 1
[1] 1 4 6 4 1
[1]  1  5 10 10  5  1
[1]  1  6 15 20 15  6  1
[1]  1  7 21 35 35 21  7  1