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?
Solution
✅ Correct Option: 2
The letters of MANAGER are A, A, E, G, M, N and R. Count the arrangements that come before MANAGER: | Case | Count | |---|---:| | Starts with A | $6!=720$ | | Starts with E | $\dfrac{6!}{2!}=360$ | | Starts with G | $\dfrac{6!}{2!}=360$ | | Starts with MA and the third letter is A, E or G | $3\times4!=72$ | | Starts with MANA and the fifth letter is E | $2!=2$ | Total $=720+360+360+72+2=1514$.