In how many different ways can the letters of the word “DIGEST” be arranged so that the vowels are at the two ends?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 48
DIGEST has six different letters, of which I and E are the vowels. The two vowels must take the two end places, and the four consonants D, G, S and T fill the four middle places in any order; each choice for the ends goes with each order of the middle.
Vowels at the ends: I first and E last, or E first and I last, \(2!=2\) ways
Consonants in the middle: \(4!=4\times3\times2\times1=24\) ways
Number of arrangements: \(2\times24=48\)