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  • Please help! 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 :

 

  • Option 1)

     \frac{11!}{\left ( 2 !\right )^{3}}

  • Option 2)

    110

  • Option 3)

    56

  • Option 4)

    59

 

Answers (1)

best_answer

As we learnt in

Number of arrangement of like and alike objects -

The number of arrangements that can be formed using n objects out of which r, q and p are identical objects then total number of arrangements=\frac{n!}{p!\ q!\ r!}

Ex. ALLAHABAD

A\rightarrow4

L\rightarrow2

\therefore\ \; \frac{9!}{4!\ 2!}

-

 

 

Theorem of Combination -

Each of the different groups or selection which can be made by taking r things from n things is called a combination.

^{n}c_{r}=\frac{(n)!}{r!(n-r)!}

- wherein

Where 1\leq r\leq n

 

 The word MEDI TERRANEAN has 

3ES, 2AS, 2NS, 1M, 1D, 1I, 1T

We need words of the form R--E

If two letters are same, we can have 3 ways.

REEE

RAAE

RNNE

If two letters are different, we can choose them in ^{8}C_{2} ways

\Rightways\ \; ^{8}C_{2}\times2!\ ways=56\ ways

Total = 59 words.

Correct option is 4.

 

 


Option 1)

 \frac{11!}{\left ( 2 !\right )^{3}}

This is an incorrect option.

Option 2)

110

This is an incorrect option.

Option 3)

56

This is an incorrect option.

Option 4)

59

This is the correct option.

Posted by

divya.saini

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