# Combinatorics - math word problems

1. Dinning room How many different combinations can we choose if there are 3 soups, 5 kinds of main dish and 2 desserts in the dining room?
2. Prime number Jan wrote any number from 1 to 20. What is the probability that he wrote the prime number?
3. Desks A class has 20 students. The classroom consists of 20 desks, with 4 desks in each of 5 different rows. Amy, Bob, Chloe, and David are all friends, and would like to sit in the same row. How many possible seating arrangements are there such that Amy, Bob, C
4. Bridge cards How many bridge hands are possible containing 4 spades,6 diamonds, 1 club, and 2 hearts?
5. Inverted nine In the hotel,, Inverted nine" each hotel room number is divisible by 6. How many rooms we can count with three-digit number registered by digits 1,8,7,4,9?
6. Perfect cubes Suppose a number is chosen at random from the set (0,1,2,3,. .. ,202). What is the probability that the number is a perfect cube?
7. Three shooters Three shooters shoot, each one time, on the same target. The first hit the target with a probability of 0.7; second with a probability of 0.8 and a third with a probability of 0.9. What is the probability to hit the target: a) just once b) at least once c
8. Practice How many ways can you place 20 pupils in a row when starting on practice?
9. Cancel fractions Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)! On the menu are 12 kinds of meal. How many ways can we choose four different meals into the daily menu?
11. Twins with friend The twins Danka and Janka went to the cinema with their friend Betka. Only six seats in the second row were available in the cinema. How many do they may sit, if the twins want to sit next to each other, Danka always to the right of Janka and Betka near on
12. Glass with icecream We have 6 kinds of ice cream and 5 kinds of fruit. We put 3 cups of ice cream and 2 fruits into each glass. How many can unique decorated glasses be?
13. Three numbers We have three different non-zero digits. We will create all 3 digits numbers from them to use all 3 figures in each number. We add all the created numbers, and we get the sum of 1554. What were the numbers?
14. To improve To improve her handwriting Paula practices writing the numbers 1 to 200 in words. How many times will she have written the word "one" in all?
15. How many 2 How many three lettered words can be formed from letters A B C D E G H if repeats are: a) not allowed b) allowed
16. Today in school There are 9 girls and 11 boys in the class today. What is the probability that Suzan will go to the board today?
17. STRESSED word Each letter in STRESSED is printed on identical cards, one letter per card and assembled in random order. Calculate the probability that the cards spell DESSERTS when assembled.
18. A jackpot How many times must I play this jackpot to win? A jackpot of seven games having (1 X 2), i. E. , home win or away win.
19. Internet anywhere In school, 60% of pupils have access to the internet at home. A group of 8 students is chosen at random. Find the probability that a) exactly 5 have access to the internet. b) At least 6 students have access to the internet
20. Combinations 7 A multi-course meal has 3 choices. 3 appetizers, 4 main courses, and 3 desserts. How many different combinations to choose from?

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