document.write( "Question 623027: On an English test, Tito must write an essay for three of five questions in Part 1, and four of six questions in Part 2. How many different combinations of questions can be chosen? \n" ); document.write( "

Algebra.Com's Answer #391806 by jsmallt9(3758) $\"\"$ $\"About$

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For Part 1 we need to find how many combinations of 3 choices can be made out of 5 options. This can be done with a tree diagram or we can use the formula for this:
\n" ); document.write( " $\"5%21%2F%283%21%2A2%21%29\"$
\n" ); document.write( "which simplifies as follows:
\n" ); document.write( " $\"%281%2A2%2A3%2A4%2A5%29%2F%28%281%2A2%2A3%29%2A%281%2A2%29%29\"$
\n" ); document.write( "

\n" ); document.write( " $\"20%2F2\"$
\n" ); document.write( " $\"10\"$

\n" ); document.write( "For Part 2, four out of 6:
\n" ); document.write( " $\"6%21%2F%284%21%2A2%21%29\"$
\n" ); document.write( " $\"%281%2A2%2A3%2A4%2A5%2A6%29%2F%28%281%2A2%2A3%2A4%29%2A%281%2A2%29%29\"$
\n" ); document.write( "

\n" ); document.write( " $\"30%2F2\"$
\n" ); document.write( " $\"15\"$

\n" ); document.write( "For the total number of ways both parts can be answered:
\n" ); document.write( "10*15 = 150 \n" ); document.write( "

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