How many different patchwork quilts, four patches long and three patches wide, can be made from five red and seven blue squares, assuming that the quilts cannot be turned over?

An urn contains 5 red balls, 4 green balls, and 1 white ball. Three are drawn simultaneously. Answer the following questions: How many ways can 1 ball of each color be drawn? How many ways can at least 1 green ball be drawn? How many ways can the same color ball be drawn?

Suppose I gave you a bag of M&M’s, but I didn’t let you see the original packaging so you can’t determine which plant made the M& M’s.  Your job is to count the number of candies of each color in your bag and figure out which plant made your bag.  What test should you do to determine this?

How many ways can the positions of center midfielder, striker, and center back be assigned from the starting ten field players of a soccer team?

How many combinations of k=5 screws is it possible to construct from n=8 different screws?  What is the number of combinations of screws?

If you pick 4 cards without replacement from a standard deck of 52 cards, how many different combinations are possible?

How many dierent 6 card hands can be dealt from a deck of 52 cards?