Probability Day 3 Worksheet

Algebra 2 Honors Probability Name________________ Find the number of possible 5-card hands that contain the cards specified. The cards are from a standard 52-card deck. 1. 5 black cards 2. 3 aces and 2 kings 3. 2 face cards (kings, queens, jacks) and 3 cards that are not face cards. 4. 5 red cards or 5 black cards 5. At most one ace 6. At least 3 fives. 7. A pizza parlor offers ten different toppings. How many different five-topping pizzas can be formed with ten toppings? (Assume no topping is used more than once.) 8. A teacher is holding tryouts for the school play. There are 15 students trying out for 7 parts in the play. Each student can play each part. In how many ways can the teacher select the students? 9. A youth indoor soccer team has 6 starting players. The starting players must consist of 3 boys and 3 girls. There are 7 boys and 6 girls on the team. Each player can play each position. In how many ways can the coach select players to start the game? 10. You have a plastic sheet that holds 9 trading cards. You want to fill the sheet with football cards consisting of 4 quarterbacks, 3 running backs, and 2 wide receivers. In your collection of cards, you have 10 quarterbacks, 7 running backs, and 8 wide receivers. In how many different ways can you select the cards? 11. A committee of four people is to be chosen from a group of 25 people. Fifteen members of the group are women. In how many different ways can you make a committee of 2 men and 2 women? 12. A committee of four people is to be chosen from a group of 25 people. Fifteen members of the group are women. In how many different ways can you make a committee of 2 or more women? 13. You have a bag of 17 red marbles, 5 blue marbles, and 8 clear ones. In how many ways can you choose 6 clear marbles and 2 red ones? 14. An ice cream parlor has a choice of 12 different toppings. You can make your own sundae by choosing 1 or more toppings. You can afford at most four toppings. How many different types of ice cream sundaes can you order? 15. Your school has scheduled three rugby games, four football games, and two soccer games. In how many ways can you go to two rugby games and one other game? 16. Seven points lie on a circle. How many inscribed triangles can be constructed having any three of these points as vertices. 17. Ten points lie on the circumference of a circle. How many inscribed quadrilaterals can be drawn having these points as vertices. 18. A school club has 15 boys and 16 girls as members. How many different 6-person committees can be selected from the membership if equal numbers of boys and girls are to be selected? 19. How many 13-card hands having exactly 11 diamonds can be dealt? 20. How many 13-card hands having exactly 11 cards from any suit can be dealt? 21. How many 5-card hands having exactly 3 aces and 2 other cards can be dealt? 22. How many 7-card hands having exactly 3 spades, 3 clubs, and 1 heart can be dealt? 23. In how many ways can 4 or more students be selected from 8 students? 24. In how many ways can up to 4 students be selected from 6 girls and 5 boys if each selected must have an equal number of girls and boys? Answers 1. 65, 780 8. 6, 435 16. 35 2. 24 9. 700 17. 210 23. 163 24. 180 3. 652, 080 10. 205, 800 18. 254, 800 4. 131, 560 11. 4, 725 19. 57, 798 5. 2, 490, 624 12. 10, 640 20. 231, 192 6. 4, 560 13. 3, 808 21. 4, 512 7. 252 14. 793 22. 1, 063, 348 15. 18