Basic Counting Practice Problems

Basic Counting- Practice Problems 1. A course catalog for the Open University of Earth lists classes via a sequence of three numbers (chosen from 0 to 9) followed by three letters in English (chosen from A to Z). How many courses can be given unique catalog numbers? Choose the best answer. a. 10×9×8×26×25×24 b. (10×10×10)+(26×26×26) c. 10³×26³ d. 10×3×26×3 2. A course catalog for the Open University of Earth lists classes via a sequence of three numbers (chosen from 0 to 9 ) followed by three letters in English (chosen from A to Z). Is this enough to offer 5 million courses? Choose the best answer. a. Yes b. No 3. Let’s say you have a class of 15 students, eight of them girls and seven boys. You want to choose a committee of four students, with two girls and two boys. How many ways can you do this? Choose the best answer. a. b. 7 8 ( )+( ) 2 2 7 8 ( )×( ) 2 2 c. 8×7+7×6 d. 8×7×7×6 4. Say you flip a fair coin eight times. What is the probability of getting four heads and four tails in any order? Choose the best answer. a. b. c. d. (12) 2 8! (8) 4 28 4!×4! 8! 24 ×24 28 5. Suppose that you play a game by rolling three dice, and your score is the highest number that appears on any of the dice. What is the probability that your score is ” 1 “? Choose the best answer. 53 a. 1 − 63 52 b. 1 − 63 c. d. 1 216 6×52 63 Revised: 05.20.21 6. What is the probability of being dealt 5 cards of the same suit (flush)? Choose the best answer. a. b. c. d. 9×45 (52) 5 4×13×12×11×10×9 (52) 5 13×12×11×10×9 (52) 5 (4)×(13) 1 5 (52) 5 7. In a drastically simplified poker game, you’re dealt just two cards. If you get a pair—that is, if the two cards are of the same denomination—you receive $50. If you get a “flush”—two cards of the same suit—the payoff is $10. What’s the expected value of the game? Choose the best answer. a. 50+10 2 b. 50 × 13×(4) 4×(13) 2 + 10 × 522 52 ( ) ( ) 2 2 3 12 c. 50 × 51 + 10 × 51 156 624 ( ( d. 50 × 52 + 10 × 52 Revised: 05.20.21 2 ) 2 )