4. Five separate awards are to be awarded to selected students from a class of 20. How many different outcomes are possible if (a) a student can receive any number of awards? (b) each student can receive at most 1 award? 5. A club consists of five men and seven women. Three members are selected at random to attend a conference. (a) Find the number of ways groups can be selected to go to the conference? (b) Find the number of ways the selected group consists of three men. (c) Find the number of ways the selected group consists of one man and two women. (d) What is the probability a group of three men go to the conference? (e) What is the probability a group of one mand and two women go to the conference? 6. Consider the experiment in which a player is dealt 5 cards from a standard deck. (a) How many starting hands are possible? (b) Find the probability that your hand consists of only hearts. 7. Fifty people purchase raffle tickets. Three winning tickets are selected at random. If first prize is $1,000, second prize is $500, and third prize is $100, in how many different ways can the prizes be awarded? 8. A signal can be formed by running different colored flags up a pole, one above the other. Find the number of different signals consisting of eight flags that can be made by using three white flags, four red flags, and one blue flag