AMATYC SML Training 9/24/09

For more problems, please visit the AMATYC website at www.amatyc.org

For solutions to last week’s problems, visit my website at www.montgomerycollege.edu/~rpenn

1. How many different arrangements of the letters of AMATYC are possible?

A. 120 B. 240 C. 360 D. 540 E. 720

2. Consider all arrangements of the letters of AMATYC with either the A’s together or the A’s on the ends. What fraction of all possible arrangements satisfies these conditions?

A. 1/5 B. 2/15 C. 1/3 D. 2/5 E. 3/5

3. Let A= {0,1,2,3,4,5,6,7,8,9}. How many 3-element subsets of A contain at least two consecutive integers?

A. 32 B. 40 C. 48 D. 56 E. 64

4. In how many ways can slashes be placed among the letters AMATYCSML to separate them into four groups with each group containing at least one letter?

A. 28 B. 56 C. 70 D. 84 E. 112

5. In how many ways can 9 identical dominos (2x1 rectangles) be used to exactly cover a 3x6 rectangle with no overlap? Assume 2 coverings are different if the 9 dominos are not in exactly the same positions.

A. 21 B. 31 C. 35 D. 41 E. 47

6. A sock drawer contains 6 identical black socks, and 4 identical brown socks. If you reach in and randomly select 2 socks, what is the probability that they will be a matched pair?

A. 2/5 B. 7/15 C. ½ D. 8/15 E. 3/5

7. A positive integer less than 1000 is chosen at random. What is the probability it is a multiple of 3, but a multiple of neither 2 nor 9?

A. 1/10 B. 1/9 C. 1/8 D. 2/9 E. 1/3

8. Teams A and B play a series of games; whoever wins the two games first wins the series. If Team A has a 70% chance of winning any single game, what is the probability that Team A wins the series?

A. .616 B. .637 C. .657 D. .700 E. .784

9. A bag holds 5 cards identical except for color. Two are red on both sides, two are black on both sides, and one is red on one side and black on the other. If you pick a card at random and the only side you can see is red, what is the probability that the other side is also red?

A. ½ B. 2/3 C. ¾ D. 4/5 E. 5/6