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  4. Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is:

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Q. Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter $M$ appears at the fourth position in any such word is:

JEE MainJEE Main 2021Permutations and Combinations

Solution:

AAEIIMNNOTX
----------- M ----------
Total words with $M$ at fourth Place $=\frac{10 !}{2 ! 2 ! 2 !}$
Total words $=\frac{11 !}{2 ! 2 ! 2 !}$
Required probability $=\frac{10 !}{11 !}=\frac{1}{11}$