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If the word “WOW” can be rearranged in exactly 3 ways (WOW,

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 118

Kudos [?]: 1899 [0], given: 397

If the word “WOW” can be rearranged in exactly 3 ways (WOW, [#permalink]  05 Aug 2018, 14:33
Expert's post
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Question Stats:

66% (00:59) correct 33% (00:37) wrong based on 6 sessions
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?

[Reveal] Spoiler: OA
34650

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Sandy
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 118

Kudos [?]: 1899 [0], given: 397

Re: If the word “WOW” can be rearranged in exactly 3 ways (WOW, [#permalink]  09 Aug 2018, 14:50
Expert's post
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: $$34,650$$.
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Sandy
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Intern
Joined: 10 Jun 2018
Posts: 32
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Kudos [?]: 16 [1] , given: 4

Re: If the word “WOW” can be rearranged in exactly 3 ways (WOW, [#permalink]  10 Aug 2018, 15:38
1
KUDOS
MISSISSIPPI has 4 M, 4 S and 2 I . Which means it can be arranged in 11!/4!*4!*2! = 34650
Re: If the word “WOW” can be rearranged in exactly 3 ways (WOW,   [#permalink] 10 Aug 2018, 15:38
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