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Max
08-18-2013, 04:18 PM
SAT math question about arrangments

In how many ways can the word ALGEBRA be arranged?

Thanks!!;);)

kadence
08-18-2013, 04:36 PM
SAT math permutations with repetition


In how many ways can the word ALGEBRA be arranged?

Having n items, where there are {n}_{1},{n}_{2},..,{n}_{k} that are identical. The number of ways to permute them is given by the following formula:

\frac{n!}{{n}_{1}!\cdot{n}_{2}!\cdot..\cdot{n}_{k} ! }

Regarding your question the above formula applies as follows

\frac{7!}{2!} (there are 7 letters from which 2 are A's)

So the total number of arrangements are \frac{7!}{2!}=\frac{2\cdot3\cdot4\cdot5\cdot6\cdot 7}{2 }=2520 \ ways

Max
08-18-2013, 04:36 PM
Thank you Kadence!