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  • Help me solve this The number of four letter words that can be formed using the letters of the word BARRACK is :

The number of four letter words that can be formed using the letters of the word BARRACK is :

  • Option 1)

    120

  • Option 2)

    144

  • Option 3)

    264

  • Option 4)

    270

 

Answers (2)

best_answer

As we learned,

 

The Number of ways of Arrangement of objects -

The number of ways of n different objects taken all at a time =\ ^{n}p_{n}=n!

- wherein

Where 0! = 1

 

 and

 

 

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!}

-

 

 

word is BARRACK  Different letters = 2A, 2R, 1B, 1C, 1K

Different 4 letter selections can be 

Case I : 2 alike of one kind, 2 alike of other kind

AARR ; Total words = \frac{4!}{2!2!}=6

Case II : 2 alike of one kind, 2 different

 _ _ _ _ ; words = ^{2}C_{1}\times ^{4}C_{2}\times \frac{4!}{2!}

alike

=2x6x12=144

Case III : All different

_ _ _ _ ; words = ^{5}C_{4}\times 4!=120

Total words = 6+144+120

=270

 


Option 1)

120

Option 2)

144

Option 3)

264

Option 4)

270

Posted by

Himanshu

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