n how many ways can the letters of the word "COMBINATION" be arranged?Choices:- 10! 11! 12! 13!
Question
In how many ways can the letters of the word "COMBINATION" be arranged?
Choices:
10!11!12!13!
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.
Similar Questions
In how many ways can the letters of the word "SUCCESS" be arranged if the two S's cannot be together?Choices:- 7!/2! - 6! 7!−6! 7!−2! 7!−5!
How many ten letter words can be formed with all the letters of the word ‘ENGAGEMENT’?Choices:- 10! 10! / (3! x 2! x 2!) 10! / (3! x 2!) 10! / 3!
Many newspapers carry a certain puzzle in which the reader must unscramble letters to form words.How many ways can the letters of RTLIOSN be arranged?
How many different words can be formed using the letters of the words “EXAMINATION‘?Options11!11! / (2! x2!)10811! / (2! X2! X2!)
In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.