SOLUTION: How many ways can the letters of the word algebra be arranged?

Question 1116419: How many ways can the letters of the word algebra be arranged?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

If all 7 letters were different, then the number of arrangements would be just 7!=5040. That is because there would be 7 choices for the first letter, then 6 choices for the second, and so on, making the total number of arrangements 7*6*5*4*3*2*1 = 7!.

But in this word, 2 of the letters are the same. Since those two letters are indistinguishable, each word in the list of 5040 arrangements appears twice -- so the number of distinct arrangements is 5040/2.

The principle extends to more complicated examples. The number of arrangements of the letters in the word Mississippi (11 letters; 4 s, 4 i, 2p) is

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