1.You roll a fair six-sided die and don't look at it. What is the probability that it is a 5 given that your friend looks and tells you that it is greater than3? Leave your answer as a fraction.

2.Suppose you draw a card, put it back in the deck, and draw another one. What is the probability that the first card is afiveand the second is aseven? (Enter your probability as a fraction.)

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3.A company wants to market different types of shampoo using color-coded bottles, lids, and label print. It hassevendifferent colors of lids, five different colors of bottles, and two different colors of print for the label available. How many different types of shampoo can the company package?

4.The following exercise refers to the toss of a pair of dice.

What is the probability that the total number of dots appearing on top is3? (Enter your probability as a fraction.)

5.The following exercise refers to the toss of a pair of dice.

What is the probability that the total number of dots appearing on top isnot5? (Enter your probability as a fraction.)

6.In how many ways can we select a committee of6people from a group of31candidates? Leave your answer in terms of factorials.