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Sagot :
There is a total of n! ways of arranging n elements on a list. In this case, the word "GATHERINGS" has 10 letters. Nevertheless, two of them are the same letter (there are two "G"s), then, half of those combinations are repeated.
Then, there is a total of 10!/2 ways to arrange those letters. Use a calculator to find the value of 10!/2:
[tex]\begin{gathered} \frac{10!}{2}=\frac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2}{2} \\ =10\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3 \\ =1,814,400 \end{gathered}[/tex]Therefore, the total amount of ways in which the letters on the word "GATHERINGS" can be arranged, is:
[tex]1,814,400[/tex]
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