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# Probability and Combinations of apples and oranges

1) A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how many ways can you get exactly 3 apples?

2) A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability of 2 cherry, 1 lemon

3) A die is rolled five times and the number of fours that come up is tallied. Find the probability of getting the given result. Exactly three fours

5) Find the requested probability. A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly three sixes?

6) Of the 2,598,960 different five-card hands possible from a deck of 52 playing cards, how many would contain the following cards? All diamonds

7) Solve the problem.How many ways can a committee of 3 be selected from a club with 12 members?

#### Solution Preview

^ stands for raised to the power of

1) A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how
many ways can you get exactly 3 apples?

Exactly 3 apples
Number of apples = 5

Ways of selecting 3 out of 5 apples = 5 C 3 = 5 x 4 x 3 / (1x2x3) = 10
With each of these ways of selecting three apples we can pick one of the three oranges
Ways of selecting 1 orange out of 3 = 3 C 1 = 3
Therefore, total number of ways = 10 x 3 = 30