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# Consider all of the distinguishable ways to arrange the letters in the word E N T E R T A I N M E N T

in a row.

In​ total, there are​ 28,828,800 such arrangements. Make sure you understand why before answering the following question.

Some of the​ 28,828,800 arrangements will have all three Es occurring​ consecutively, but will have none of the Ns occurring consecutively. An example of such an arrangement​ is:

N R A E E E N T N I M T T.

How many arrangements have both of these​ properties?

Given word : E N T E R T A I N M E N T Number of all possible arrangement = 3 ! 3 ! 3 ! 1 3 ! = 28,828,800 Now... View the full answer

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