Use permutations and combinations to compute probabilities of compound events and solve problems.
Count distinct arrangements when some objects repeat
Problem
Start with \(7!\) orders for BALLOON, then divide by \(2!\) for the two Ls and \(2!\) for the two Os.
Big Picture
What this problem is really about
Repeated objects make the all-labeled factorial overcount visible arrangements. We’ll inventory the total letters and each repeated group, start with all positional orders, divide by the internal permutations of identical copies, and evaluate the corrected distinct count.
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