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Re: If the word “WOW” can be rearranged in exactly 3 ways (WOW,
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09 Aug 2018, 14:50
Explanation
This is a combinatorics problem, and the WOW example is intended to make it clear that any W is considered identical to any other W—switching one W with another would not result in a
different combination, just as switching one S with another in MISSISSIPPI would not result in a different combination.
Therefore, solve this problem using the classic combinatorics formula for accounting for subgroups among which order does not matter:
Total...number...of...items!First..group!×Second...group!.
Because MISSISSIPPI has 11 letters, including 1 M, 4 S’s, 4 I’s, and 2 P’s:
11!1!×4!×4!×2!
Now expand the factorials and cancel; use the calculator for the last step of the calculation: 34,650.