1. Suppose that the sample space is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and that outcomes are equally likely. Compute the probability of the event E: "a number divisible by 3".
2. How many 6-letter codes can be formed using the letters A, B, C, D, E, F, G, H, and I. Repeated letters are allowed.
531,441
10,077,696
60,480
3. A committee is to be formed consisting of 5 men and 6 women. If the committee members are to be chosen from 8 men and 9 women, how many different committees are possible?
140
4704
12,376
406,425,600
4. How many different license plates can be made using 3 letters followed by 3 digits selected from the digits 0 through 9, if letters and digits may be repeated?
36
260
17,576,000
9
5. How many arrangements of answers are possible in a multiple-choice test with 7 questions, each of which has 3 possible answers?
840
210
35
2187
6. Mary finds 9 fish at a pet store that she would like to buy, but she can afford only 5 of them. In how many ways can she make her selection? How many ways can she make
7560; 840
126; 70
3024; 1680
7. An exam consists of 9 multiple-choice questions and 6 essay questions. If the student must answer 5 of the multiple-choice questions and 3 of the essay questions, in how many ways can the questions be chosen?
810
2520
261,273,600
1,814,400
8. How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0? No digit can be used more than once.
302,400
5040
151,200
210
9. How many different license plates can be made using 3 letters followed by 3 digits selected from the digits 0 through 9, if digits may be repeated but letters may not be repeated?
12,654,720
17,576,000
15,600,000
3095.2381
10. In how many ways can 7 people each have different birth months?
84
35,831,808
3,991,680
792
11. How many 5-card poker hands consisting of three 10's and two cards that are not 10's are possible in a deck?
4512
5304
2256
2652
12. How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 6 forwards, 8 midfield players, and 8 defensive players?
646,646
78,400
67,737,600
146
13. How many different license plates can be made using 3 letters followed by 4 digits selected from the digits 0 through 9, if neither letters nor digits may be repeated?
47,174,400
78,624,000
175,760,000
546,000
14. How many 6-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digit cannot be 0? Repeated digits are allowed.
60,480
272,160
900,000
531,441
15. 12 different books are to be arranged on a shelf. How many different arrangements are possible?
239,500,800
39,916,800
479,001,600
12
16. A student must choose 1 of 4 mathematics electives, 1 of 5 science electives, and 1 of 9 programming electives. How many possible course selections are there?
20 course selections
360 course selections
180 course selections
18 course selections
17. A group of 12 friends goes bowling. How many different possibilities are there for the order in which they play if the youngest person is to bowl first?
12
39,916,800
479,001,600
11