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Combinatorial Problems: Seating Arrangements, Probability, and Pizza Orders

Explore fascinating combinatorial problems involving seating arrangements, probability calculations, and toppings for pizzas. This compilation addresses diverse scenarios: determining the number of ways to arrange friends in a theater, selecting members for a competition, and calculating pizza options based on size and toppings. Delve into marble selections with specific color requirements and the arrangement of letters in a word. Each problem is a practical application of combinations and permutations, ensuring engaging practice in probability and combinatorial mathematics.

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Combinatorial Problems: Seating Arrangements, Probability, and Pizza Orders

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  1. Beth, Jill, Angel, and Lenny found 4 seats together at a crowded theater. In how many ways can they be seated? 24

  2. The math team has 13 members. In how many ways can 4 be selected to participate in the team competition? 715

  3. How many different one topping pizzas can be ordered if the restaurant offers 3 sizes, 2 crusts and 7 toppings? 42

  4. How many different pizzas with any number of toppings can be ordered if the restaurant offers 3 sizes, 2 crusts and 7 toppings? 768

  5. There are 8 red, 4 yellow and 6 blue marbles in a bag. In how many ways can 5 marbles be chosen from the bag? 8568

  6. There are 8 red, 4 yellow and 6 blue marbles in a bag. In how many ways can 5 marbles be chosen from the bag if you want 2 red and 3 yellow marbles? 112

  7. There are 8 red, 4 yellow and 6 blue marbles in a bag. In how many ways can 5 marbles be chosen from the bag if you at least 1 blue marble? 7776

  8. In how many ways can the letters of the word FOOLPROOF be arranged? 7560

  9. What is the probability of choosing a King or a club when choosing one card from a standard deck? 4/13

  10. What is the probability of get a perfect test paper if you guess on a multiple choice test that has 10 questions and 5 answer options for each question? 1/9765625

  11. Candy Dish 3 orange plain 4 blue plain 2 blue peanut 5 yellow peanut Pull two out in a row and get an orange and then a peanut. 3/26

  12. Candy Dish 3 orange plain 4 blue plain 2 blue peanut 5 yellow peanut Pull 4 out at once and get 2 blue and 2 yellow. 150/1001

  13. Candy Dish 3 orange plain 4 blue plain 2 blue peanut 5 yellow peanut Take one and get a blue or a peanut. 11/14

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