document.write( "Question 1046062: what is the number of ways of seating 3 men and 5 women in a row if there is no restrictions \n" ); document.write( "

Algebra.Com's Answer #661556 by KMST(5328) $\"\"$ $\"About$

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Consider how the women are lined up .
\n" ); document.write( "There are $\"5%21=5%2A4%2A3%2A2=120\"$ different ways to line up those $\"5\"$ women.
\n" ); document.write( "Considering how the men are lined up,
\n" ); document.write( "there are $\"3%21=3%2A2=6\"$ ways to line them up.
\n" ); document.write( "We could sit all 3 men at one end,
\n" ); document.write( "in what we could say are positions 1, 2, and 3, of the row of $\"5%2B3=8\"$ people.
\n" ); document.write( "There are other ways to pick where the men would go.
\n" ); document.write( "Any set of 3 position numbers picked out of the 8 positions would do.
\n" ); document.write( "There are $\"8%2A7%2A6%2F%283%2A2%29=56\"$ such combinations of 8 taken 3 at at time.
\n" ); document.write( "So, out total number of choices is
\n" ); document.write( " $\"120%2A6%2A56=40320\"$ .
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