Word problem permutations and combinations

Question

A basketball team consists of some guards and six forewards. If there are 420 ways to select two guards and three foreward to start the game, then how many guards on the team are there.

Answer 1

Hi Clare,

Cool question!  

 

If you have 6 possible forwards and you are choosing 3 of them to start, then there are C(6, 3), which means 6 choose 3, ways to do that.  C(6, 3) = 20.

 

The total number of ways to choose the starting team is 420 and there are 20 ways to choose the forwards.  If you divide the 420 by the 20, this gives 21 which represents the number of ways to choose the 2 guards.  So, you are looking for x such that C(x, 2) = 21.  Since 21 is relatively small, trial and error might be the best way to go.  This gives the answer x = 7.  So, you have 7 guards to choose from.

 

Hope this helps.