How many 7 letter words with or without meaning can be formed out of the letters of the word, “ENCAPSULATION”?Choices:- 78280 6282620 8648640 56600

The word "ENCAPSULATION" has 13 letters in total. However, the letters 'N' and 'A' are repeated twice.

The formula to calculate the number of ways to arrange 'n' items (where some items are repeated) is n! / (p1! * p2! * ... * pk!), where 'n' is the total number of items, and p1, p2, ..., pk are the frequencies of the repeated items.

In this case, n = 7 (since we want to form 7-letter words), and the frequencies of the repeated items are 2 (for 'N' and 'A').

So, the number of ways to form 7-letter words out of the letters of the word "ENCAPSULATION" is 13P7 = 13! / (2! * 2! * (13-7)!) = 8648640.

So, the correct answer is 8648640.