JEE MainMathematicsPermutations and CombinationsMCQ+4 / −1
If the four letter words (need not be meaningful ) are to be formed using the letters from the word “MEDITERRANEAN” such that the first letter is R and the fourth letter is E, then the total number of all such words is :
- A
- B110
- C56
- D59
View written solutionFree
Correct answer: D
-
Count the letters in
MEDITERRANEANThe word is:
Frequency of letters:
- each
-
Apply the position restrictions
We need 4-letter words such that:
- first letter is
- fourth letter is
So the form is:
After fixing one and one , the remaining available letters are:
- each
Thus, for the 2nd and 3rd positions, we must choose an ordered pair from this remaining multiset.
-
Count all possible ordered pairs for positions 2 and 3
Distinct available letter types are: i.e. types.
We count ordered pairs in two cases.
Case 1: Both letters different
- Choose the 2nd letter in ways.
- Choose the 3rd letter in ways.
Total:
Case 2: Both letters same
This is possible only for letters having at least 2 copies left.
Such letters are:
( has only 1 left, so is not possible.)
Hence same-letter pairs possible are:
Total:
-
Total number of words
-
Check options
- A: not equal to
- B: ❌
- C: ❌
- D: ✅
Therefore, the correct answer is:
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