Problem

How many distinct permutations can be formed using the letters of the word "CONNECTION"?
There are distinct permutations.
(Type a whole number.)

Answer

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Answer

Final Answer: The number of distinct permutations that can be formed using the letters of the word 'CONNECTION' is \(\boxed{151200}\).

Steps

Step 1 :The word 'CONNECTION' has 10 letters, with the letter 'N' appearing 3 times, the letter 'O' appearing 2 times, and the letter 'C' appearing 2 times. The rest of the letters each appear once.

Step 2 :The formula for the number of permutations of a multiset (a set in which members are allowed to appear more than once) is given by: \[\frac{n!}{n1! * n2! * ... * nk!}\] where n is the total number of items, and n1, n2, ..., nk are the numbers of each type of item.

Step 3 :In this case, n = 10, n1 = 3 (for 'N'), n2 = 2 (for 'O'), and n3 = 2 (for 'C').

Step 4 :So, the number of distinct permutations is: \[\frac{10!}{3! * 2! * 2!}\]

Step 5 :Final Answer: The number of distinct permutations that can be formed using the letters of the word 'CONNECTION' is \(\boxed{151200}\).

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