Discrete math Probability problems A large bowl contains 32

Discrete math

Probability problems

A large bowl contains 32 marbles of which 20 are Blue, 10 are Green, and 2 are Red. A chance process consists of drawing three marbles at random, one after the other and without replacement and recording the colors of the marbles. Thus an outcome could be Blue first, then Red, and then another Blue last. It is not possible to draw Red, Red, Red as there are only 2 Red marbles. Give a clear description of the sample space. You may draw a diagram, or you may list several elements of the sample space, but your description must be clear. What is the probability of drawing the colors Red, Blue, Green in any order? What is the probability of drawing at least one Blue marble? What is the probability that the third marble drawn is Red? A group of 15 students are to be assigned seats in a classroom with 18 desks. The desks cannot be moved and are arranged in three rows, with 6 desks in each row. In how many different ways can the students be assigned to the desks? Note that in each possible assignment, there will be 3 desks that remain empty, unassigned to any student. Remember to include a brief indication of your counting strategy. Sally has 12 identical red balls and 1 green ball. She is to distribute these 13 balls to 5 children. If each child receives least one red ball; in how many different ways is it possible to distribute the 13 balls to the 3 children? You must include a brief indication of your counting strategy?

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