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How many arrangements of the word DARWIN begin and end with a vowel?

1 Answer

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Answer:

The number of arrangements of the word DARWIN beginning and ending with a vowel = 48 ways

Step-by-step explanation:

The number of letters in DARWIN = 6

The vowels are "A" and "I"

Number of vowels = 2

Number of ways of arranging the two vowels that will be at the beginning and end = 2! = 2 x 1 = 2 ways

There are 4 remaining letters after excluding the vowels

Number of ways of arranging the 4 remaining letters = 4!

Number of ways of arranging the 4 remaining letters = 4 x 3 x 2 x 1

Number of ways of arranging the 4 remaining letters = 24 ways

Therefore, the number of arrangements of the word DARWIN beginning and ending with a vowel = 2 x 24

The number of arrangements of the word DARWIN beginning and ending with a vowel = 48 ways

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