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Probability question: rearranging letters?
What is the total number of ways that the following string of characters can be rearranged-
AAAAAABBBBBBCCCCCCDDDDDD
EEEEEEFFFFFFGGGGGG
We have 6 copies each of all the letters A through G all in one string (I had to split the line to get it all to display). We want to pull them out in random order. What is the total number of letter sequences that can be generated in this way?
1 Answer
- 10 years agoFavorite Answer
You can always calculate these types of questions by:
counting the total number of characters you have = 42
and the number of repeat of each letters
You always take the factorial of total number divided by the number of times a letter has repeated (factorial).
Since A, B, C, D, E, F, G all repeats 6 times. We divide 42 factorial by 6! 7 times. (7 letters)
42! /(6!*6!*6!*6!*6!*6!*6!) = 1.4007*10^31 different arrangements.
Hope this helps!
