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)

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.

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