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Easy

Question

Number of ways to rearrange the letters of the word CHEESE is

  1. 100    
  2. 115    
  3. 119    
  4. 120    

Hint:

Total number of arrangements of the letters of the word CHEESE = Number of arrangements of 6 things taken all at a time, of which 3 are of one kind

The correct answer is: 119


    The letter CHEESE contains 3 E's
    Thus, Total number of arrangements of the letters of the word CHEESE = Number of arrangements of 6 things taken all at a time, of which 3 are of one kind = fraction numerator 6 factorial over denominator 3 factorial end fraction space equals space 120

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    T o t a l space A r r a n g e m e n t s space equals fraction numerator X factorial over denominator left parenthesis x 1 factorial right parenthesis left parenthesis x 2 factorial right parenthesis left parenthesis x 3 factorial right parenthesis...... left parenthesis x n factorial right parenthesis end fraction
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    T o t a l space A r r a n g e m e n t s space equals fraction numerator 17 factorial over denominator left parenthesis 7 factorial right parenthesis left parenthesis 6 factorial right parenthesis left parenthesis 4 factorial right parenthesis space space end fraction space equals space 4084080 space space
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    T o t a l space A r r a n g e m e n t s space equals fraction numerator X factorial over denominator left parenthesis x 1 factorial right parenthesis left parenthesis x 2 factorial right parenthesis left parenthesis x 3 factorial right parenthesis...... left parenthesis x n factorial right parenthesis end fraction
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    Before solving the question, we are going to assume that all the balls of the same color are identical. This means that one red ball is identical to another red ball. Similarly, one black ball is identical to all the other black balls and one white ball will be similar to other white balls. Now, we are given that out of 17 balls, 7 of them are black, 6 are red and 4 are white. Now, we will arrange these balls in a row. The formula by which we can arrange the total number of entities which contain similar entities is given as:
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