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AP EAMCET · Maths · Permutation Combination

The letters of the word 'QUESTION' are arranged in a row at random. The probability that there are exactly two letters between \(\mathrm{Q}\) and \(\mathrm{S}\) is

  1. A \(\frac{1}{14}\)
  2. B \(\frac{5}{7}\)
  3. C \(\frac{1}{7}\)
  4. D \(\frac{5}{28}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{5}{28}\)

Step-by-step Solution

Detailed explanation

The given word is 'QUESTION', let E be the event that there are exactly two letters between \(Q\) and \(S\). Here, number of sample space, \(n(S)=8 \text { ! }\) number of possible events, \(n(E)={ }^6 P_2 \times 2 ! \times 5 \text { ! }\) \(\therefore \quad\) Required…