n how many ways can the letters of the word "COMBINATION" be arranged?Choices:- 10! 11! 12! 13!
Question
Solution
The word "COMBINATION" has 11 letters in total. However, some letters are repeated. The letter 'O' is repeated 2 times, the letter 'N' is repeated 2 times, and the letter 'I' is repeated 2 times.
The formula to calculate the number of ways to arrange n items (where some items are repeated) is n! / (r1! * r2! * ... * rk!), where r1, r2, ..., rk are the number of times each item is repeated.
In this case, n = 11 (the total number of letters), r1 = 2 (the number of times 'O' is repeated), r2 = 2 (the number of times 'N' is repeated), and r3 = 2 (the number of times 'I' is repeated).
So, the number of ways to arrange the letters of the word "COMBINATION" is 11! / (2! * 2! * 2!) = 11! / 8 = 4989600.
So, the correct answer is not in the given choices.
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