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COUNTING AND ODERING TECHNIQUES
1.
TRACK MEET AMONG SCHOOLS A , B AND C
| First Place(5 points) | Second Place(3 points) | Third Place(1 point) | |
| Event I | A | ||
| Event II | A | B | |
| Event III | C |
A partially completed scorecard for a track meet is shown above . Schools A, B and C each entered one person in each of the three events and there were no ties. What is one possible total score for school C (Assume that all points are awarded in each event.)
2. In a stack of six cards , each card is labeled with a different integer 0 through 5. If two cards are selected at random without replacement , what is the probability that their sum will be 3 ?
3. A bag contains a number of pieces of candy of which 78 are red , 24 are brown, and the remainder are yellow . If the probability of selecting a yellow piece of candy from this bag at random is 1/3 , how many yellow pieces of candy are in the bag ?
4. There are 120 red marbles and 80 blue marbles in a bag that contains 200 marbles . If only blue marbles are to be added to the bag so that the probability of randomly drawing a blue marble from the bag becomes 2/3 , how many blue marbles must be added to the bag ?
5. There are 3 roads from Plattsville to Ocean Heights and 4 roads from Ocean Heights to Bay Cove . If Martina drives from Plattsville Bay Cove and back , passes through Ocean Heights in both directions , and does not travel any road twice , how many different routes for the trip are possible.
6. A barrel contains only apples and oranges . There are twice as many apples as oranges . The apples are either red or yellow , and 4 times as many apples are red as are yellow. If one piece of fruit is to be drawn at random from the barrel , what is the probability that the piece drawn will be a yellow apple ?
7. A teacher is to be assigned to teach 5 different courses in 5 different class periods on Mondays. If exactly one course meets each period , how many different assignments of courses to these class periods are possible for Mondays ?
8.
| Quiz Score | Number of Students Who Received That Score |
| 0 | 3 |
| 1 | 6 |
| 2 | 7 |
| 3 | 4 |
A class of 20 students took a 3-question quiz. The table shows the possible scores on this quiz and the number of students who received each of these scores.If one of the students is picked at random , what is the probability that that student’s quiz score will be greater than 1 ?
9. Of the students in a certain homeroom , 9 are in the school play , 12 are in the orchestra , and 15 are in the choral group . If 5 students participate in exactly 2 of the 3 activities and all other students participate in only 1 activity, how many students are in the homeroom ?
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