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 vowel, and each letter can be used only once?\nOptions:\n(A) 20\n(B) 40\n(C) 120\n(D) 60\n(E) 10
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Vowel: E O\nConsonants: V R M N T\nFirst letter can be filled in 2 Ways ( As the question states that first letter has to be a vowel)\nFifth letter can be filled in 1 Ways ( As the question states that the last letter has to be a vowel)\nNow since each letter can be used only once, and 2 letters out of 7 letters are already used in First and fourth letter\nSecond letter can be filled in 5 Ways\nThird letter can be filled in 4 Ways\nSo, Total number of ways = 2 Ways x 5 Ways x 4 ways x 1 ways = 40
The final answer: (B).
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