How many different words can be formed using the letters of the words “EXAMINATION‘?Options11!11! / (2! x2!)10811! / (2! X2! X2!)
Question
How many different words can be formed using the letters of the words “EXAMINATION"?
Options:
11!11! / (2! x2!)10811! / (2! X2! X2!)
Solution
The word "EXAMINATION" has 11 letters in total. However, the letters 'A' and 'I' are repeated twice.
To find the number of different words that can be formed, we use the formula for permutations of a multiset: n! / (r1! * r2! * ... * rk!), where n is the total number of items, and r1, r2, ..., rk are the numbers of each type of repeated item.
In this case, n = 11 (the total number of letters), r1 = 2 (the number of 'A's), and r2 = 2 (the number of 'I's).
So, the number of different words is 11! / (2! * 2!) = 11! / (2! x 2!) which is the correct answer.
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