If all the letters of the word MANAGER are arranged to form 7-letter words (with or without meaning), and all such words are arranged lexicographically (as in a dictionary), how many of these words…
Question and options
If all the letters of the word MANAGER are arranged to form 7-letter words (with or without meaning), and all such words are arranged lexicographically (as in a dictionary), how many of these words will precede the word MANAGER?
- 1518
- 1514
- 1512
- 1516
Answer and explanation
Correct answer: B - 1514
Sorted letters: A,A,E,G,M,N,R. Words starting with A: 6! = 720; with E: 6!/2! = 360; with G: 360 (total 1440). Starting MA: third letter A/E/G gives 3 x 4! = 72. Starting MANA: fifth letter E gives 2! = 2, and MANAG then E,R is MANAGER itself. 1440+72+2 = 1514 words come before it.
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