5. A special card set has 12 cards. in how many different ways can the cards be placed into groups consisting of 4 cards in each group?

Question

Really need answers to all these questions from the textbook from homework, i have no idea how to answer any of them and i would like step by step with answer as i have test coming up.

Answer 1

This is a combination problem (order doesn't matter).  Said another say, "12 items, choose 4".  There is a formula to use for these problems, as you do not want to have to list out the various combinations when the numbers are high.

 

12C4 = 12! / (8!4!) = (12*11*10*9*8!) / (8! *4*3*2*1)

Cancel the 8! from the numerator and denominator.

Cancel the 12 in the numerator with the 4*3 in the denominator.

Reduce the 10 in the numerator with the 2 in the denominator to make 5 and you have:

 

(11*5*9)/1 = 495