# Combinatorics - math word problems

1. Win in raffle The raffle tickets were sold 200, 5 of which were winning. What is the probability that Peter, who bought one ticket will win?
2. Football league In the football league is 16 teams. How many different sequence of results may occur at the end of the competition?
3. Box and whisker plot Construct a box and whisker plot for the given data. 56, 32, 54, 32, 23, 67, 23, 45, 12, 32, 34, 24, 36, 47, 19, 43
4. 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?
5. PIN - codes How many five-digit PIN - code can we create using the even numbers?
6. Ten dices When you hit ten dices at the same time you get average 35. How much do you hit if every time you get six, you're throwing the dice again?
7. Candies In the box are 12 candies that look the same. Three of them are filled with nougat, five by nuts, four by cream. At least how many candies must Ivan choose to satisfy itself that the selection of two with the same filling? ?
8. Hockey game In the hockey game was made 6 goals. Czech played against Finland. Czechs won 4:2. In what order to fall goals? How many game sequence was possible during the game?
9. Five-digit Find all five-digit numbers that can be created from numbers 12345 so that the numbers are not repeated and then numbers with repeated digits. Give the calculation.
10. Three-digit numbers How many three-digit numbers are from the numbers 0 2 4 6 8 (with/without repetition)?
11. Hockey match The hockey match ended with result 3:1. How many different storylines may have the match?
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. Neighborhood I have 7 cups: 1 2 3 4 5 6 7. How many opportunities of standings cups are there if 1 and 2 are always neighborhood?
14. Lion or virgin We toss coin, every throw fits lion or a virgin with equal probability 1/2. Determine how much at least we have to make throws that with probability 0.9 lion fell at least once.
15. Three digits number 2 Find the number of all three-digit positive integers that can be put together from digits 1,2,3,4 and which are subject to the same time has the following conditions: on one positions is one of the numbers 1,3,4, on the place of hundreds 4 or 2.
16. 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?
17. One green In the container are 45 white and 15 balls. We randomly select 5 balls. What is the probability that it will be a maximum one green?
18. travel agency Small travel agency offers 5 different tours at honeymoon. What is the probability that the bride and groom choose the same tour (they choose independently)?
19. Olympics In how many ways can be placed 6 athletes on the podium at the Olympics? Depend on the color of the metal.
20. Raffle How many raffle tickets must be purchased by Peter in raffle with issued 200 tickets if he wants to be sure win at least 3 price? In the raffle draws 30 prices.

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