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The binomial coefficient C(n, r) = n!/(r!(n−r)!) counts the ways to choose r items from n when order does not matter. Permutations P(n, r) = n!/(n−r)! count the same selections when order does matter, so P = C × r!.
Combinations
C(n, r) = n! / (r!(n − r)!)
Permutations
P(n, r) = n! / (n − r)!
210, while P(10, 4) = 5040 because the four chosen items can be ordered in 4! = 24 ways.
Choosing which r to include is the same as choosing which n − r to leave out.