Question 388973: Find the number of ways the letters of each word can be arranged. The word is "ALBUQUERQUE" I got 1,663,200. But it seems wrong. D:
Found 2 solutions by haileytucki, richard1234:
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! 11!
The factorial (!) of a positive integer n is the product of all positive integers less than or equal to n.
11*10*9*8*7*6*5*4*3*2*1
Multiply 11 by 10 to get 110.
110*9*8*7*6*5*4*3*2*1
Multiply 110 by 9 to get 990.
990*8*7*6*5*4*3*2*1
Multiply 990 by 8 to get 7920.
7920*7*6*5*4*3*2*1
Multiply 7920 by 7 to get 55440.
55440*6*5*4*3*2*1
Multiply 55440 by 6 to get 332640.
332640*5*4*3*2*1
Multiply 332640 by 5 to get 1663200.
1663200*4*3*2*1
Multiply 1663200 by 4 to get 6652800.
6652800*3*2*1
Multiply 6652800 by 3 to get 19958400.
19958400*2*1
Multiply 19958400 by 2 to get 39916800.
39916800*1
Multiply 39916800 by 1 to get 39916800.
39916800
Answer by richard1234(7193)  (Show Source):
You can put this solution on YOUR website! There are 11! ways to arrange the letters. However, if the U's, Q's, E's are indistinguishable, we have to divide to account for overcounting. There are three U's, 2 Q's, and 2 E's, so we divide by 3!2!2!. 11!/(3!2!2!) = 1,663,200.
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