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What is the probability that a word formed by randomly rearr

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What is the probability that a word formed by randomly rearr [#permalink] New post 14 May 2019, 00:42
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What is the probability that a word formed by randomly rearranging the letters of the word ALGAE is the word ALGAE itself?

(A) \(\frac{1}{120}\)

(B) \(\frac{1}{60}\)

(C) \(\frac{2}{7}\)

(D) \(\frac{2}{5}\)

(E) \(\frac{1}{30}\)
[Reveal] Spoiler: OA

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Re: What is the probability that a word formed by randomly rearr [#permalink] New post 14 May 2019, 08:00
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Consider the following steps to manually calculate the scenario:

1) Draw a ____ for Each Selection to be Made and Label any Dictated Restrictions for the Selection. In this case there will be a selection of five letters.

2) Determine most efficient method to properly and specifically make selection based on problem and consider whether selecting this or that or this and that.
In this case, the word must be spelled as A | L | G | A | E with A and L and G and A and E in that exact order, thus requiring multiplication to determine the number of possible acceptable permutations and total permutations.

3) Then insert the number or available options at moment of selection one blank at a time.
For the acceptable permutation of A | L | G | A | E there are 2 possible A's to select for the first blank, then 1 possible L, then 1 possible G, then 1 remaining possible A, and finally 1 possible E. Multiply all of those values together to determine that there are 2 x 1 x 1 x 1 x 1 = 2 possible ways to spell out ALGAE with the available letters.

Then, to find the total possible permutations of the letters multiply by the number of available options at the moment of each of the five selections or 5 x 4 x 3 x 2 x 1 = 5! = 120 total possible permutations.

4) Finally, set the probability. Probability is defined as the desired number of outcomes / total possible number of outcomes. In this case there are 2 desired outcomes of ALGAE divided by 120 total possible arrangements of the five letters or 2/120, which simplifies to 1/60 and matches choice B.
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Re: What is the probability that a word formed by randomly rearr   [#permalink] 14 May 2019, 08:00
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