Combinatorial and Factorial Functions: A Crash Review

The combinatorial function C(n,k) ["n choose k"]: The factorial function n! ["n factorial"]:
I presume enough familiarity with college algebra that pkqn-k is recognized as "p to the kth power, times q to the power of n-k".

Sk=0..m means the sum of the terms indexed by k, where k is an integer from 0 to the (positive) integer m>0. If the pattern for the terms is declared elsewhere, it may be replaced with +...+ .

The combinatorial function C(n,k) is defined as n!/[k!(n-k)!], where n! is the factorial function.

In turn, the factorial function n! is defined as the product of the consecutive integers from 1 to n.

For all exercises involving variables, one variant is to deliberately work enough concrete examples to develop a physical intuition for the problem statement.

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