Question

There are how many ways to arrange the letters in GATHERINGS

Answer 1

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:

`\begin{gathered} (10!)/(2)=(10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2)/(2) \\ =10\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3 \\ =1,814,400 \end{gathered}`

Therefore, the total amount of ways in which the letters on the word "GATHERINGS" can be arranged, is:

`1,814,400`