How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a consonant and the last letter has to be a consonant, and each letter can be used only once?\nOptions:\n(A) 21\n(B) 42\n(C) 1500\n(D) 600\n(E) 720 Stream of consciousness:
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Vowel: E O\nConsonants: V R M N T\nFirst letter can be filled in 5 Ways ( As the question states that first letter has to be a consonant)\nFifth letter can be filled in 4 Ways ( As the question states that the last letter has to be a consonant)\nNow since each letter can be used only once, and 2 letters out of 7 letters are already used in First and Fifth letter\nSecond letter can be filled in 5 Ways\nThird letter can be filled in 4 Ways\nFourth letter can be filled in 3 Ways\nSo, Total number of ways = 5 Ways x 5 Ways x 4 ways x 3 ways x 5 ways = 1500
Thus, the answer is (C).
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