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What is the total number of different 10-letter arrangements that can be formed using the letters in the word FORGETTING?

Sagot :

Using the arrangements formula, it is found that 907,200 arrangements can be formed using the letters in the word FORGETTING.

What is the arrangements formula?

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

When there are repeating elements, with the number of times given by [tex]n_1, n_2, \cdots, n_n[/tex], the number of arrangements is given by:

[tex]A_n^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]

In this problem, the word FORGETTING has 10 letters, of which G and T repeat twice, hence the number of arrangements is given by:

[tex]A_{10}^{2,2} = \frac{10!}{2!2!} = 907,200[/tex]

More can be learned about the arrangements formula at https://brainly.com/question/25925367

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