Oh, dude, it's like a blast from the past with these math problems. So, with the word "Adam," you can arrange it in 4! ways, which is 4x3x2x1, giving you a total of 24 possible arrangements. But, like, who knew arranging letters could be so entertaining, right?
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If you have 4 DIFFERENT letters, there are 24 ways - this is equal to 4! (that is, the factorial of 4). Because of the two repeated letters, if you do this, you get every valid combination repeated twice (i.e., by exchanging one "a" with the other "a" you get an identical combination). Therefore the real number of arrangements is only one-half that value.
362,880 ways
15
Six.
There are 11!/[2!*2!*2!) = 4,989,600 ways.
If you have three DIFFERENT letters, you can arrange them in 3! = 1 x 2 x 3 = 6 different ways.