# Combinatorics - math word problems

1. Three-digit
How many three-digit natural numbers is greater than 321 if no digit in number repeated?
2. 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?
3. Class - boys and girls
In the class are 60% boys and 40% girls. Long hair has 10% boys and 80% girls. a) What is the probability that a randomly chosen person has long hair? b) The selected person has long hair. What is the probability that it is a girl?
4. The camp
At the end of the camp a 8 friends exchanged addresses. Any friend gave remaining 7 friends his card. How many addresses they exchanged?
5. Friends in cinema
5 friends went to the cinema. How many possible ways can sit in a row, if one of them wants to sit in the middle and the remaining's place does not matter?
6. Three digits number
From the numbers 1, 2, 3, 4, 5 create three-digit numbers that digits not repeat and number is divisible by 2. How many numbers are there?
7. Chess
How many different ways can initiate a game of chess (first pass)?
8. Three digits number
How many are three-digit integers such that in they no digit repeats?
9. Combinations
How many different combinations of two-digit number divisible by 4 arises from the digits 3, 5 and 7?
10. A three-digit numbers
Determine the total number of positive three-digit numbers that contain a digit 6.
11. Hockey players
After we cycle five hockey players sit down. What is the probability that the two best scorers of this crew will sit next to each other?
12. The dice
What is the probability of events that if we throw a dice is rolled less than 6?
13. Seven-segmet
Lenka is amused that he punched a calculator (seven-segment display) numbers and used only digits 2 to 9. Some numbers have the property that their image in the axial or central symmetry was again give some number. Determine the maximum number of three-
14. Lottery
Fernando has two lottery tickets each from other lottery. In the first is 973 000 lottery tickets from them wins 687 000, the second has 1425 000 lottery tickets from them wins 1425 000 tickets. What is the probability that at least one Fernando's ticket
15. Trainings
The table contains tennis training schedule for Saturday's younger students during the winter indoor season. Before the start of the summer season is preparing a new training schedule. Tomas Kucera will be able to practice only in the morning, sisters Kov
16. 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.
17. Variations
Determine the number of items when the count of variations of fourth class without repeating is 42 times larger than the count of variations of third class without repetition.
18. Logik game
Letter game Logik is a two player game, which has the following rules: 1. The first player thinks five-letter word in which no letter is not repeated. 2. The second player writes a five-letter word. 3. The first player answers two numbers - the first numb
The voltage station is every day changing the master password, which consists of three letters. Code generation process does not change and is based on the following procedure: The following letters (A) to (I) correspond to different numbers from 1 to 9.
20. Pairs
From the five girls and four boys teachers have to choose one pair of boy and girl. A) How many such pairs of (M + F)? B) How many pairs where only boys (M + M)? C) How many are all possible pairs?

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