WASHINGTON STATE MATHEMATICS COUNCIL 2000 MIDDLE SCHOOL MATH OLYMPIAD Session II: EIGHTH GRADE PROBABILITY & STATISTICS Make sure you include proper units in your answer!

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1. A pocket full of change consists of 5 nickels, 2 dimes, and 1 quarter. Two coins are randomly chosen from the pocket without replacement. What is the probability that their combined value is 15 cents? Express your answer as a common fraction.

2. There is an unlimited supply of cubes in four colors: red (R), blue (B), white (W), and green (G). Cubes of all four colors are to be placed together in a single row in such a way that:

(1) no two cubes of the same color are next to each other, i.e., RR is not allowed;

(2)successive colors cannot repeat, i.e., RW can only happen once.

How many cubes can be placed this way in one row?

3. A survey was taken from a group of 983 families to find which of them had:

(1) a computer,

(2) a microwave,

(3) a CD player, and

(4) a connection to the Internet.

It was found that no family was completely without any of the items. Also 481 families had at least two of the items, 345 families had at least 3 of the items, and 264 families had all 4 items.

(a) How many items did all 983 families have together?

(b) How many families had exactly 2 of the items?

4. Determine a set of 6 two-digit even whole numbers which have a sum of 246, a median of 41, and no mode.

5. There are four hats in a checking room. The four men who own these hats receive their hats at random. What is the probability that exactly three out of the 4 men get their hats?