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If the word “WOW” can be rearranged in exactly 3 ways (WOW,
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05 Aug 2018, 14:33
05 Aug 2018, 14:33
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Question Stats:
74% (01:37) correct
25% (01:38) wrong based on 35 sessions
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If the word “WOW” can be rearranged in exactly 3 ways (WOW, OWW, WWO), how many different arrangements of the letters in “MISSISSIPPI” are possible?
Show: :: OA
34650
Re: If the word “WOW” can be rearranged in exactly 3 ways (WOW,
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09 Aug 2018, 14:50
09 Aug 2018, 14:50
Expert Reply
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:
\(\frac{Total...number...of...items!}{First..group! \times Second...group!}\).
Because MISSISSIPPI has 11 letters, including 1 M, 4 S’s, 4 I’s, and 2 P’s:
\(\frac{11!}{1! \times 4! \times 4! \times 2!}\)
Now expand the factorials and cancel; use the calculator for the last step of the calculation: \(34,650\).
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:
\(\frac{Total...number...of...items!}{First..group! \times Second...group!}\).
Because MISSISSIPPI has 11 letters, including 1 M, 4 S’s, 4 I’s, and 2 P’s:
\(\frac{11!}{1! \times 4! \times 4! \times 2!}\)
Now expand the factorials and cancel; use the calculator for the last step of the calculation: \(34,650\).
Re: If the word “WOW” can be rearranged in exactly 3 ways (WOW,
[#permalink]
10 Aug 2018, 15:38
10 Aug 2018, 15:38
1
MISSISSIPPI has 4 M, 4 S and 2 I . Which means it can be arranged in 11!/4!*4!*2! = 34650
