document.write( "Question 1111234: Suppose that a class contains 15 boys and 30 girls, and that 10 students are to be selected at random for a special assignment. Find the probability that exactly 3 boys will be selected. \n" ); document.write( "

Algebra.Com's Answer #726222 by rothauserc(4718) $\"\"$ $\"About$

You can put this solution on YOUR website!
There are 45 students and we select 10 students from that group
\n" ); document.write( ":
\n" ); document.write( "There are 45C10 ways to do that selection process, where nCr = n! / (r! * (n-r)!)
\n" ); document.write( ":
\n" ); document.write( "Therefore,
\n" ); document.write( ":
\n" ); document.write( "45C10 = 45! / (10! * (45-10)!) = 3,190,187,286 ways
\n" ); document.write( ":
\n" ); document.write( "We want to find the number of ways we can choose 3 boys from the 15 boys
\n" ); document.write( ":
\n" ); document.write( "15C3 = 15! / (3! * (15-3)!) = 455 ways to choose 3 boys from the 15 boys
\n" ); document.write( ":
\n" ); document.write( "Now, exactly 3 boys implies that there are exactly 7 girls in the group of 10 selected
\n" ); document.write( ":
\n" ); document.write( "There are 30C7 = 30! / (7! * (30-7)!) = 2,035,800 ways to choose the 7 girls
\n" ); document.write( ":
\n" ); document.write( "Probability that exactly 3 boys will be selected = (455*2035800)/3190187286 = 0.29035568
\n" ); document.write( ":
\n" ); document.write( " \n" ); document.write( "

\n" );