document.write( "Question 584053: In how many ways can you select 4 essay questions out of 10? I just need a basic formula to begin this problem! Thanks.... \n" ); document.write( "
Algebra.Com's Answer #372670 by solver91311(24713)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "It depends on whether order matters. That is, is Q1, Q2, Q3, Q4 the same or different from Q2, Q1, Q3, Q4?\r
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\n" ); document.write( "\n" ); document.write( "If order matters, that is if the two examples given above are actually considered different selections, then you want where is calculated by . The idea being, in your example, that there are 10 ways to pick the first question and for each of these 10 ways there are 9 ways to pick the second question, so 10 times 9, and then for those 90 ways there are 8 ways to pick the third question, and so on. The math is thus:\r
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\n" ); document.write( "\n" ); document.write( "On the other hand, if order doesn't matter, using the above arithmetic overcounts by a factor of the number of ways you can arrange 4 things, namely 4!. Hence, if order doesn't matter you need another factor in the denominator: You want where is calculated by .\r
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\n" ); document.write( "\n" ); document.write( "And the arithmetic for your problem becomes:\r
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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