document.write( "Question 1037588: In how many ways can the letters of the word irrational be arranged\r
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Algebra.Com's Answer #652185 by purpleoj(8) $\"\"$ $\"About$

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The answer depends on whether you need just the amount of possible ways or whether they need to be distinguishable.\r
\n" ); document.write( "\n" ); document.write( "You calculate the number of possible ways by simply writing $\"+10%21+\"$ , which, in expanded form, means $\"+10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1+\"$ , which equals 3628800, which is your number of possible ways.\r
\n" ); document.write( "\n" ); document.write( "However, because there are three instances of the same letter (there are 2 \"a\"s, 2 \"r\"s, and 2 \"i\"s), you must divide by the factorial of number of times each letter occurs seperately to make each way distinguishable, otherwise you will have identical looking combinations of letters.\r
\n" ); document.write( "\n" ); document.write( " $\"+10%21%2F%282%212%212%21%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "This will give you 453600.\r
\n" ); document.write( "\n" ); document.write( "Your two answers will be 3628800 for a nondistinguishable permutation, or 453600 for a distinguishable permutation.\r
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