If we rearrange the letters in the word "strange", what is the ratio of rearrangements where the vowels are not together to the rearrangements where they are together?
1 Answer
Explanation:
Let's first consider how many different ways we can arrange the letters in the word strange. There are 7 letters and so we can arrange them
How many of those ways will have the vowels together?
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There are 2 vowels and they can be arranged 2 different ways: AE and EA.
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There are 6 different places in the word these two vowels can be: positions 1, 2; 2, 3; 3, 4...all the way to 6, 7.
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That leaves the 5 remaining letters to be arranged in whatever arrangement around the two vowels in
#5!# ways.
And so there are:
This means there are:
We can therefore set up the ratio
