A used car lot has four green flags, three red flags and two blue flags in a bin. In how many ways can the owner arrange these flags on a wire stretched across the lot?
Question
A used car lot has four green flags, three red flags and two blue flags in a bin. In how many ways can the owner arrange these flags on a wire stretched across the lot?
Solution
This is a permutation problem involving identical objects. The formula for permutations of n objects taken r at a time is nPr = n! / (n-r)!. However, when dealing with identical objects, we need to adjust this formula to account for the fact that the order of identical objects doesn't matter.
The formula for permutations of n objects where there are n1 of one type, n2 of another, etc. is n! / (n1! * n2! * ...).
In this case, there are 9 flags in total (4 green, 3 red, 2 blue). So, n = 9.
The number of each type of flag is n1 = 4 (green), n2 = 3 (red), n3 = 2 (blue).
Plugging these values into the formula gives us:
9! / (4! * 3! * 2!) = 1260
So, there are 1260 ways to arrange the flags on the wire.
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