document.write( "Question 1065678: a. How many distinguishable arrangements are there using the
\n" ); document.write( "letters from the word STATISTICS?
\n" ); document.write( "b. Let’s define a substring to be an arrangement with a specific
\n" ); document.write( "condition. Consider the substrings that contain the 3 T’s in a
\n" ); document.write( "row … for example SAISICSTTT, or TTTSASSICI would be two such
\n" ); document.write( "substrings. How many of the arrangements in part (a) contain
\n" ); document.write( "none of these substrings? \n" ); document.write( "

Algebra.Com's Answer #681155 by Edwin McCravy(20055) $\"\"$ $\"About$

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a. How many distinguishable arrangements are there using the
\n" ); document.write( "letters from the word STATISTICS?

STATISTICS is a 10-letter word.  If we could tell the S's apart,\r\n" );
document.write( "the I's apart, and the T's apart, the answer would be 10!  But\r\n" );
document.write( "since we cannot, we must divide the 10! by the product of the \r\n" );
document.write( "factorials of the number of S's, I's, and T's, or 3!*2!*3!\r\n" );
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\n" ); document.write( "b. Let’s define a substring to be an arrangement with a specific
\n" ); document.write( "condition. Consider the substrings that contain the 3 T’s in a
\n" ); document.write( "row … for example SAISICSTTT, or TTTSASSICI would be two such
\n" ); document.write( "substrings. How many of the arrangements in part (a) contain
\n" ); document.write( "none of these substrings?

First we calculate the number of distinguishable substrings, then\r\n" );
document.write( "subtract what we get from 50400.\r\n" );
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document.write( "The distinguishable substrings are the distinguishable arrangements\r\n" );
document.write( "of ACIISSS(TTT), where the (TTT) is considered as a single character.\r\n" );
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document.write( "That's 8 characters, where the two I's and the the three S's are\r\n" );
document.write( "indistinguishable, so the number of distinguishable substrings is\r\n" );
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document.write( "So we subtract 50400-3360 = 47040\r\n" );
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document.write( "Edwin

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