document.write( "Question 892395: Classify the problem as a permutations, a combinations, or neither.
\n" ); document.write( "A student is asked to answer 11 out of 13 questions on a exam. In how many ways can she select the questions to be answered?(Order is not important).\r
\n" ); document.write( "\n" ); document.write( "(b) In how many ways can a chairperson and a vice chairperson be selected from a committee of 15 senators?\r
\n" ); document.write( "\n" ); document.write( "(c)How many permutations are there of the following word?
\n" ); document.write( "Combinatorics\r
\n" ); document.write( "\n" ); document.write( "(d) Tarot cards are used for telling fortunes, and in a reading, the arrangement of the cards is as important as the cards themselves. How many different readings are possible if four cards are selected from a set of eight Tarot cards?\r
\n" ); document.write( "\n" ); document.write( "(E)A state's license plate consist of four letters followed by three numerals, and 246 letter arrangements are not allowed. How many plates can the state issue?
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Algebra.Com's Answer #540621 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
(a) A student is asked to answer 11 out of 13 questions on a exam. In how many
\n" ); document.write( "ways can she select the questions to be answered?(Order is not important).
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document.write( "C(13,11) = C(13,13-11) = C(13,2) = \"13%2A12%2F%282%2A1%29\" = \"156%2F2\" = 78\r\n" );
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\n" ); document.write( "(b) In how many ways can a chairperson and a vice chairperson be selected from a
\n" ); document.write( "committee of 15 senators?
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document.write( "P(15,2) = 15*14 = 210 \r\n" );
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\n" ); document.write( "(c)How many permutations are there of the following word?
\n" ); document.write( "COMBINATORICS
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document.write( "If the 2 C's, the 2 I's, and the 2 O's were distinguishable, the answer would be\r\n" );
document.write( "P(13,13) = 13! since it is a 13-letter word.  However since they are not\r\n" );
document.write( "distinguishable, we must divide by the factorial of each:\r\n" );
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document.write( "\"13%21%2F%282%212%212%21%29\" = \"%2813%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%28%282%2A1%29%282%2A1%29%29\" = 778377600   \r\n" );
document.write( "

\n" ); document.write( "(d) Tarot cards are used for telling fortunes, and in a reading, the arrangement
\n" ); document.write( "of the cards is as important as the cards themselves. How many different
\n" ); document.write( "readings are possible if four cards are selected from a set of eight Tarot
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document.write( "P(8,4) = 8*7*6*5 = 1680 \r\n" );
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\n" ); document.write( "(E)A state's license plate consist of four letters followed by three numerals,
\n" ); document.write( "and 246 letter arrangements are not allowed. How many plates can the state
\n" ); document.write( "issue?
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document.write( "The number of possible letter arrangement, allowed or not, are\r\n" );
document.write( "26*26*26*26 = 264 = 11881376\r\n" );
document.write( "[Notice that permutations do not work because we can use each letter more than\r\n" );
document.write( "once.]\r\n" );
document.write( "From that we subtract the 246 arrangements which are not allowed.\r\n" );
document.write( "That's 11881376-246 = 11881130\r\n" );
document.write( "The number of digit arrangements is 10*10*10 = 103.\r\n" );
document.write( "[Again permutations do not work because we can use the same digits more \r\n" );
document.write( "than once. \r\n" );
document.write( "So we multiply them tobether and get 11881376*1000 = 11881376000.\r\n" );
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document.write( "Edwin
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