1. In how many ways can three men and three women be seated at a round table if Jane and Janet cannot sit next to each other?

2. A penny, a nickel, a dime, a quarter, and a half dollar were tossed simultaneously. In how many ways can two of the coins fall heads and three of the coins fall tails?

3. How many ways can a group of six people sit at a round table?

4. How many ways can the letters in the word ALGEBRA be arranged?

5. In how many ways can seven persons sit around a circular table if 2 people insist on sitting together?

6. In how many ways can eight different colored beads be arranged on a bracelet?

7. In how many ways can fifteen students be partitioned into three teams of five each?

8. How many ways are there to arrange four charms on a bracelet?

9. How many different signals, each consisting of six flags hung in a vertical line, can be formed from three blue flags, two green flags, and one gray flag?

10. How many ways are there to arrange the letters in the word MISSISSIPPI be arranged if the four S’s must be together?

11. In how many ways can four men and four women sit at a round table so that no two men are adjacent?

12. In how many ways can three red, four blue, and two green pens be distributed among nine students seated in a row if each student receives one pen?

13. Find the number of six letter permutations that can be formed from the letters in the word SHOPPER.

14. How many five-digit integers can be made if 1 and 2 may each be used twice, and 3 may be used once.

15. How many ways are there to arrange seven people in a circle if John and Jim have to sit together?

16. In how many ways can three apples, two oranges, four pears, and one banana be given to 10 children if each child receives a piece of fruit?

17. The Chicago Bulls will be playing in the NBA Championship series 17. The Chicago Bulls will be playing in the NBA Championship series. In the series, the first team to win four games wins the championship. How many ways can the series go six games before determining a champion?

18. If no two books are alike, in how many ways can two red, three green and four blue books be arranged on a shelf so that all the books of the same color are together?

19. How many ways are there for seven people to sit together at a round table if Mary and Joan cannot sit next to each other?

20. How many different three-digit numbers can be made with 3 fours, 4 twos, and 2 threes?