PERMUTATIONS
In how many different ways can 7 bicycles be parked if there are 5 available parking spaces?
P(n,r) = n! / (n - r)!
P(7,5) = 7! / (7 - 5)!
P(7,5) = 7! / 2!
P(7,5) = 7 • 6 • 5 • 4 • 3 • 2! / 2!
P(7,5) = 7 • 6 • 5 • 4 • 3
P(7,5) = 2520 ways
In a certain general assembly, three major prizes are at the stake. In how many ways can the first second and third prizes be drawn from a box containing 20 names?
P(n,r) = n! / (n - r)!
P(20,3) = 20! / (20 - 3)!
P(20,3) = 20! / 17!
P(20,3) = 20 • 19 • 18 • 17! / 17!
P(20,3) = 20 • 19 • 18
P(20,3) = 6840 ways
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