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In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?

Q.11.    In how many ways can the letters of the word ASSASSINATION be arranged
             so that all the S’s are together?

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In the word ASSASSINATION, we have

number of S =4

number of A =3

number of I= 2

number of N =2 

Rest of letters appear at once.

Since all words have to be arranged in such a way that all the S are together so we can assume SSSS as an object.

The single object SSSS with other 9 objects is counted as 10.

These 10 objects can be arranged in  (we have 3 A's,2 I's,2 N's)

                                                                                                   =\frac{10!}{3!2!2!}  ways.

Hence, requires the number of ways of arranging letters

                                                                                 =\frac{10!}{3!2!2!}=151200

 

 

 

 

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