Combination Problems

• A box contains 3 defective and 7 good lightbulbs. If two lightbulbs are selected at random determine the probability that
  • Both are good
  • Both are bad
  • one is good and one is bad.
• A bag contains four red balls and five green balls. You select three balls at random. Find the probability that
  • All three are green
  • All three are red
  • At least one is red.
  • At least one is green.
  • Exactly two balls are the same color.
• Each of the digits 0-9 are written on a slip of paper and the slips of paper are put into a hat. If three slips are selected at random, find the probability that all three are greater than 5.
• You are dealt 10 cards from a standard deck. Find the probability that all 5 are red.
• A full house in poker consists of three of one kind and two of another kind in a five card hand. Find the probability of geting three kings and two fives.
• A car rental agency has 10 midsized and 15 compact cars. If six cars are selected at random find the probability that
  • All six are midsized
  • 2 are midsized and 4 are compact
  • 3 midsized and 3 compact
  • At least 1 compact car.