document.write( "Question 1122537: A bag contains two 1-dollar bills, three 5-dollar bills, and two 10-dollar bills. An experiment consists of drawing three random bills from the bag simultaneously. Considering an outcome to be the three selected bills, the experiment has C(7,3)=35 equally likely outcomes in its sample space. Let E be the event that at most one 5-dollar bill was drawn. What is n(E)? \n" ); document.write( "

Algebra.Com's Answer #738938 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "n(E) is the number of ways of choosing either none of the three $5 bills AND 3 of the four others, OR one of the three $5 bills AND two of the four others:

\n" ); document.write( "C(3,0)*C(4,3)+C(3,1)*C(4,2) = 1*4+3*6 = 4+18 = 22.

\n" ); document.write( "If you are just learning how to solve problems like this, notice that the ANDs indicate multiplications and the ORs indicate additions.

\n" ); document.write( "When learning to solve problems like this, it is good practice to verify that those possibilities plus the others give the correct total of 35 total ways to choose 3 of the 7 bills.

\n" ); document.write( "two $5 bills and one of the others: C(3,2)*C(4,1) = 3*4 = 12
\n" ); document.write( "three $5 bills and none of the others: C(3,3)*C(4,0) = 1*1 = 1

\n" ); document.write( "22+12+1 = 35 CHECK! \n" ); document.write( "

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