Give stream of consciousness and then the final answer. How many 4 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once?
Options:
(A) 21
(B) 42
(C) 120
(D) 600
(E) 200
Vowel: E O
Consonants: V R M N T
First letter can be filled in 2 Ways ( As the question states thatfirst letter has to be a vowel)
Fourth letter can be filled in 5 Ways ( As the question states thatthe last letter has to be a consonant)
Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and fourth letter
Second letter can be filled in 5 Ways
Third letter can be filled in 4 Ways
So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 5 ways = 200
The final answer: (E).