document.write( "Question 356904: Mrs. Smith has twenty children in her class. In how many ways can she choose 4 members and a captain to form a quiz team? \n" ); document.write( "

Algebra.Com's Answer #254952 by jsmallt9(3758) $\"\"$ $\"About$

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This problem is easier if you consider the problem in two steps:
\n" ); document.write( "1. Pick a team of 5 members
\n" ); document.write( "2. From the members of that team, pick a captain.

\n" ); document.write( "For picking a team, this is a problem of figuring out how many sets of 5 are possible when picking from a group of 20. This is a combination which we can find using:
\n" ); document.write( " $\"%2820%2A19%2A18%2A17%2A16%29%2F%281%2A2%2A3%2A4%2A5%29\"$
\n" ); document.write( "The 4*5 cancels the 20 and the 2*3 (or 6) cancels with the 18 (leaving 3):
\n" ); document.write( "19*3*17*16 = 15504
\n" ); document.write( "So there are 15504 possible teams of 5 which can be formed from the 20 children.

\n" ); document.write( "Now we can pick the captain. On each of these 15504 teams, there are 5 possible choices for captain. So there are 15504*5 = 77520 possible ways of picking a team of 5 with one of the five being captain.

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