Solved: Justify the equations in either by deriving them
Chapter 9, Problem 7E(choose chapter or problem)
Problem 7E
Justify the equations in either by deriving them from formulas in Example or by direct computation from Theorem Assume m, n, k, and r are integers.
Example
Values of Think of Theorem as a general template: Regardless of what nonnegative numbers are placed in the boxes, if the number in the lower box is no greater than the number in the top box, then
Use Theorem to show that for all integers n ≥ 0,
Solution
Theorem
The number of subsets of size r (or r-combinations) that can be chosen from a set of n elements, , is given by the formula
or, equivalently
where n and r are nonnegative integers with r ≤ n.
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