Combinatorial number - examples - page 3

1. Class pairs
In a class of 34 students, including 14 boys and 20 girls. How many couples (heterosexual, boy-girl) we can create? By what formula?
2. Cards
The player gets 8 cards of 32. What is the probability that it gets a) all 4 aces b) at least 1 ace
3. Sum or product
What is the probability that two dice fall will have the sum 7 or product 12?
4. Combinations of sweaters
I have 4 sweaters two are white, 1 red and 1 green. How many ways can this done?
5. The confectionery
The confectionery sold 5 kinds of ice cream. In how many ways can I buy 3 kinds if order of ice creams does not matter?
6. Disco
On the disco goes 12 boys and 15 girls. In how many ways can we select four dancing couples?
7. Roses 2
Aunt Rose went to the flower shop to buy a bouquet with three roses. The flower shop had white, yellow and red roses. How many different flowers bouquet can a flower make for Aunt Rose create? Write all the bouquet options.
8. Cards
From a set of 32 cards we randomly pull out three cards. What is the probability that it will be seven king and ace?
9. VCP equation
Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0
10. Balls
The urn is 8 white and 6 black balls. We pull 4 randomly balls. What is the probability that among them will be two white?
11. Ice cream
Annie likes much ice cream. In the shop are six kinds of ice cream. In how many ways she can buy ice cream to three scoop if each have a different flavor mound and the order of scoops doesn't matter?
12. Hockey match
The hockey match ended with result 3:1. How many different storylines may have the match?
13. First class
The shipment contains 40 items. 36 are first grade, 4 are defective. How many ways can select 5 items, so that it is no more than one defective?
14. Combinations
From how many elements we can create 990 combinations 2nd class without repeating?
15. Volleyball
8 girls wants to play volleyball against boys. On the field at one time can be six players per team. How many initial teams of this girls may trainer to choose?
16. Division
Division has 18 members: 10 girls and 6 boys, 2 leaders. How many different patrols can be created, if one patrol is 2 boys, 3 girls and 1 leader?
17. Two aces
From a 32 card box we randomly pick 1 card and then 2 more cards. What is the probability that last two drawn cards are aces?
18. Prize
How many ways can be rewarded 9 participants with the first, second and third prize in a sports competition?
19. Competition
15 boys and 10 girls are in the class. On school competition of them is selected 6-member team composed of 4 boys and 2 girls. How many ways can we select students?
20. Combinations
If the number of elements increase by 3, it increases the number of combinations of the second class of these elements 5 times. How many are the elements?

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