# Combinatorics - math word problems

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. Combinations of sweaters I have 4 sweaters two are white, 1 red and 1 green. How many ways can this done? Kamila wants to change the password daliborZ by a) two consonants exchanged between themselves, b) changes one little vowel to such same great vowel c) makes this two changes. How many opportunities have a choice?
5. Football team Football team has in store black, purple and orange shirts, blue and white shorts and striped and gray socks. How many different outfits players may start?
6. 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?
7. Digits How many five-digit numbers can be written from numbers 0.3,4, 5, 7 that is divided by 10 and if digits can be repeated.
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. Disco On the disco goes 12 boys and 15 girls. In how many ways can we select four dancing couples?
10. 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.
11. Variations 4/2 Determine the number of items when the count of variations of fourth class without repeating is 600 times larger than the count of variations of second class without repetition.
12. Balls We have n identical balls (numbered 1-n) is selected without replacement. Determine 1) The probability that at least one tensile strength number coincides with the number of balls? 2) Determine the mean and variance of the number of balls, which coincides.
13. VCP equation Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0
14. 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?
15. Cards Suppose that are three cards in the hats. One is red on both sides, one of which is black on both sides, and a third one side red and the second black. We are pulled out of a hat randomly one card and we see that one side of it is red. What is the probabi
16. Three-digit How many three-digit natural numbers do not have the number 7?
17. 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?
18. Metals In the Hockey World Cup play eight teams, determine how many ways can they win gold, silver and bronze medals.
19. Hockey match The hockey match ended with result 3:1. How many different storylines may have the match?
20. Probability What are the chances that the lottery, in which the numbers are drawn 5 of 50 you win the first prize?

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