document.write( "Question 1199271: All of the arrangements of the letters in the word ALGEBRA are written on a list, one of these arrangments selected at random. What is the probability that the arrangement contains a double-A \n" ); document.write( "

Algebra.Com's Answer #833084 by ikleyn(52802) $\"\"$ $\"About$

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\n" ); document.write( "All of the arrangements of the letters in the word ALGEBRA are written on a list,
\n" ); document.write( "one of these arrangments selected at random.
\n" ); document.write( "What is the probability that the arrangement contains a double-A
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document.write( "There are 7 letters in the word \"ALGEBRA\", in all; of them, only letter \"A\" repeats twice.\r\n" );
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document.write( "The table below shows the number of distinguishable arrangements with  1, 2, 3, 4, 5, 6 and 7 letters.\r\n" );
document.write( "In the 2nd and 3rd columns, the formula is used nPk = n*(n-1)*...*(n-k+1).\r\n" );
document.write( "In the second column, n=5.  In the third column, n=6.\r\n" );
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document.write( "      # of     # of arrangements  # of arrangements   # of arrangements \r\n" );
document.write( "     letters      without \"A\"       with one \"A\"        with two \"A\"s\r\n" );
document.write( "     k  used         5Pk                6Pk                 \r\n" );
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document.write( "       1              5                  6                    -\r\n" );
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document.write( "       2             20                 30                    1\r\n" );
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document.write( "       3             60                120                    3\r\n" );
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document.write( "       4            120                360                   12\r\n" );
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document.write( "       5            120                720                   60\r\n" );
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document.write( "       6             -                 720                  360\r\n" );
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document.write( "       7             -                  -                  2520\r\n" );
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document.write( "     Total          325               1956                 2956\r\n" );
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document.write( "    The probability that the arrangement contains a double-A =  =  = 0.5643  (rounded).\r\n" );
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document.write( "The \"1\", added in the denominator, is for empty arrangement.\r\n" );
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document.write( "ANSWER.  The probability that the arrangement contains a double-A is 0.5643  (rounded).\r\n" );
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\n" ); document.write( "\n" ); document.write( "The major lesson to learn from this solution is how to organize your thoughts and your calculations.\r
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