Q&A - Ask Doubts and Get Answers
Q

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)
Views

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

 

 

 

 

 

 

Exams
Articles
Questions