Suppose an urn contains red, green, blue, and black marbles. Suppose you draw marbles from the urn 5 times, replacing the marble each time, and count how many of each color you get. How many possible outcomes are there? Justify your answer.

You are buying 10 t-shirts and there are 8 different colors to choose from. How many ways can you choose the 10 t-shirts if you can have as many of each type as you would like?

This game is called “Get Negative”.  Roll two dice (record these in the order you roll them), and then do then do the following:  take the first number rolled and subtract 2 times the second number rolled. Regardless of who rolls, Player A gets 3 points if the product is greater than or equal to 0 (i.e. it is zero or positive); Otherwise Player B gets 1 points. The players may or may not take turns rolling the dice as it does not matter who is rolling. Any player may score on any roll, and every roll will result in a score.   Play the game by rolling the dice 25 times. For each turn, keep a record of both dice and the resulting answer and the points scored, according to the rules above. Tally the points and calculate the final score for each player.  Remember, someone gets a point for each turn, depending on the numbers rolled. (One does not have to be rolling to receive the points.)  (Note: you may test the game by yourself by doing all of the 25 rolls yourself and just giving the…

A dish contains 2 yellow, 4 red, 5 purple, 2 green, and 3 orange candies.  How many sets of 7 candies include at least 3 purple ones?