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

Question

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

Canvas Classes · Accepted Answer

🧠 Symmetry — P(M at Specific Position) = (Count of M's) / (Total Letters)

Read the question carefully. The word EXAMINATION has  letters: E, X, A, M, I, N, A, T, I, O, N. Letter frequencies:
- A: 
- I: 
- N: 
- E, X, M, T, O:  each

Total:  letters.

We arrange all  letters into a "word" and ask: what is the probability that the letter M is at position ?

Here is the key symmetry argument. In a random arrangement of these  letters, each LETTER (not each letter slot) is equally likely to occupy

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