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If 4 letter words are formed using letters of the word ‘MORADABAD’, then the probability that D comes exactly once in the 4 letter word is

Options

  1. A146 313
  2. B213 313
  3. C167 313
  4. D520 621

Correct answer

A. 146 313

Step-by-step solution

Total cases = 4 letter word is formed by using either 3 identical letter and 1 distinct letter or 2 alike of one kind and 2 alike of 2 n d kind or 2 alike, 2 distinct or 4 distinct Number of ways for 3 alike and 1 distinct = C 1 1 × C 5 1 × 4 ! 3 ! = 20 Number of ways for 2 alike and 2 alike = C 2 2 × 4 ! 2 ! 2 ! = 6 Number of ways for 2 alike and 2 distinct = C 2 1 × C 5 2 × 4 ! 2 ! = 240 Number of ways for 4 distinct = C 6 4 × 4 ! = 360 The total number of ways = 20 + 6 + 240 + 360 =

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