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:
Solutions · 1
Official solution
EXAMINATION has 11 letters: A\times 2, I\times 2, N\times 2, and E,X,M,T,O once each.
Total arrangements =2!2!2!11!.
Arrangements with M fixed at position 4: arrange remaining 10 letters (still A\times 2,I\times 2,N\times 2 among them): 2!2!2!10!.
\[P = \frac{10!/(2!2!2!)}{11!/(2!2!2!)} = \frac{1}{11}\]