Question:
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 :
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 :
Updated On: Apr 1, 2026
- $\frac{11!}{(2!)^3}$
- $110$
- $56$
- $59$
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The Correct Option is D
Solution and Explanation
M, EEE, D. I, T, RR, AA, NN
\(\frac{R}{ }--\frac{E}{ }\)
Two empty places can be filled with identical letters [EE, AA, NN] \(\Rightarrow\) 3 ways
Two empty places, can be filled with distinct letters [M, E, D, I, T, R, A, N] \(\Rightarrow ^{8}P_{2}\)
\(\therefore\) Number of words 3+56=59
or
\(3+^{8}P_{2}=59\)
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.