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