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  • In how many of the distinct permutations of the letters in MISSISSIPPI do the four I' s not come together?

Q.10.    In how many of the distinct permutations of the letters in MISSISSIPPI do the  
            four I’s not come together?

Answers (1)

best_answer

In the given word MISSISSIPPI, I appears 4 times, S appears 4 times, M appears 1 time and P appear 2 times.

Therefore, the number of distinct permutations of letters of the given word is 

                                                                                                              =\frac{11!}{4!4!2!}

                                                                                                              =\frac{11\times 10\times 9\times 8\times 7\times 6\times 5\times 4!}{4!4!2!}

                                                                                                              =\frac{11\times 10\times 9\times 8\times 7\times 6\times 5}{4\times 3\times 2\times 2}

                                                                                                              =34650

 

There are 4 I's in the given word. When they occur together they are treated as a single object for the time being. This single object with the remaining 7 objects will be 8 objects.

These 8 objects in which there are 4Ss and 2Ps can be arranged in  \frac{8!}{4!2!}=840 ways.

 The number of arrangement where all I's occur together = 840.

 

Hence, the distinct permutations of the letters in MISSISSIPPI  in which the four I's do not come together=34650-840=33810

 

 

 

 

 

 

Posted by

seema garhwal

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