Question:
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 :
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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Count all arrangements of EXAMINATION (with repeated A, I, N) and those with M fixed in position 4.
Updated On: Nov 4, 2026
- \(\frac{1}{66}\)
- \(\frac{1}{11}\)
- \(\frac{1}{9}\)
- \(\frac{2}{11}\)
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The Correct Option is B
Solution and Explanation
EXAMINATION has 11 letters: E, X, M, T, O once each and A, I, N twice each.
Total arrangements \(=\frac{11!}{2!\,2!\,2!}\).
With M fixed at the 4th place, the remaining 10 letters (A, I, N twice each; E, X, T, O once) can be arranged in \(\frac{10!}{2!\,2!\,2!}\) ways.
Probability \(=\frac{10!}{11!}=\frac1{11}\).
Answer: (2) \(\frac{1}{11}\)
Total arrangements \(=\frac{11!}{2!\,2!\,2!}\).
With M fixed at the 4th place, the remaining 10 letters (A, I, N twice each; E, X, T, O once) can be arranged in \(\frac{10!}{2!\,2!\,2!}\) ways.
Probability \(=\frac{10!}{11!}=\frac1{11}\).
Answer: (2) \(\frac{1}{11}\)
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