document.write( "Question 1203283: The letters of the word MATHEMATICS are written, one on each of 11 separate cards. The cards are laid out in a line.
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Algebra.Com's Answer #838741 by Edwin McCravy(20055) $\"\"$ $\"About$

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The letters of the word MATHEMATICS are written, one on each of 11 separate
\n" ); document.write( "cards. The cards are laid out in a line.
\n" ); document.write( "a. Calculate the number of different arrangements of these letters.

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document.write( "If all 11 letters of MATHEMATICS were distinguishable, the answer would be 11!.\r\n" );
document.write( "But since the two M's are indistinguishable we must divide by 2!. Same for the A's and T's.\r\n" );
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document.write( "So that's

\n" ); document.write( "b. Determine the probability that the vowels are placed together.

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document.write( "We begin by finding the permutations of consonants MTHMTCS.\r\n" );
document.write( "There are \r\n" );
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document.write( "Then for every arrangement of consonants, for instance for MTHMTCS, we place 8\r\n" );
document.write( "blanks.\r\n" );
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document.write( "____M____T____H____M____T____C____S____\r\n" );
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document.write( "and pick one of the 8 blanks to put all 4 vowels together in.  We can do that in\r\n" );
document.write( "8 ways.\r\n" );
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document.write( "The 4 vowels AEAI can be arranged in  ways.\r\n" );
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document.write( "So the number of successful ways is (1260)(8)(12) = 120960 ways.\r\n" );
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document.write( "So the desired probability is \r\n" );
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document.write( "Edwin

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