# Combinatorics - math word problems

1. 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?
2. Triangles Five sticks with a length of 2,3,4,5,6 cm. How many ways can you choose three sticks to form three sides of a triangle?
3. Blocks There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?
4. Diagonals What x-gon has 54 diagonals?
5. Dice We throw 10 times a play dice, what is the probability that the six will fall exactly 4 times?
6. Three students Three students independently try to solve the problem. The first student will solve a similar problem with a probability of 0.6, the second student will solve at a probability of 0.55, and the third will solve at a probability 0.04. The problem is resolve
7. Bridge cards How many bridge hands are possible containing 4 spades,6 diamonds, 1 club, and 2 hearts?
8. Cancel fractions Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)!
9. Dd 2-digit numbers Find all odd 2-digit natural numbers compiled from digits 1; 3; 4; 6; 8 if the digits are not repeated.
10. Normal distribution GPA The average GPA is 2.78 with a standard deviation of 4.5. What are students in the bottom the 20% having what GPA?
11. Seven Seven friends agree to send everyone a holiday card. How many postcards were sent?
12. Dice We throw five times the dice. What is the probability that six fits exactly twice?
13. Find the 2 Find the term independent of x in the expansion of (4x3+1/2x)8
14. Combinations 6 6 purses 9 flaps 12 straps Every combination must include 1 purse, 1 flap, and 1 strap. How many are possible combinations?
15. Subsets How many 19 element's subsets can be made from the 26 element set?
16. Raffle There are 200 draws in the raffle, but only 20 of them win. What is the probability of at least 4 winnings for a group of people who have bought 5 tickets together?
17. How many How many double-digit numbers greater than 30 we can create from digits 0, 1, 2, 3, 4, 5? Numbers cannot be repeated in a two-digit number.
18. 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 o
19. Test The teacher prepared a test with ten questions. The student has the option to choose one correct answer from the four (A, B, C, D). The student did not get a written exam at all. What is the probability that: a) He answers half correctly. b) He answers
20. 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,

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