# Combinatorics - examples - page 7

1. 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?
2. Throw
We throw 2 times with 2 dices. What is the probability that the first roll will fall more than sum of 9 and the second throw have sum 3 or does not have the sum 4?
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. 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.
5. Confectionery
The village markets have 5 kinds of sweets, one weighs 31 grams. How many different ways a customer can buy 1.519 kg sweets.
6. Normal Distribution
At one college, GPA's are normally distributed with a mean of 3.1 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.7 and 3.5?
7. Four swords
Obelix has three helmets, four swords and five shields. How many swords must make at the blacksmith forge Metallurgix to be able to walk another 90 days in unique armor?
Determine the number of integers from 1 to 106 with ending four digits 2006.
9. Lines
How many lines can be draw with 8 points, if three points lie on one line and the other any three points do not lie on the same line?
10. 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.
11. Doctor 2
A doctor noted the Diastolic Blood Pressure (DBP) of a large number of patients. Later, he scrambled the data to keep the privacy of his patients. Based on the scrambled dataset, he finds that the lower inner fence is equal to 50 and the upper inner fenc
12. Sum 10
What is the probability that two dice throw twice in a row will result the sum of 10?
13. 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.
14. Fish tank
A fish tank at a pet store has 8 zebra fish. In how many different ways can George choose 2 zebra fish to buy?
15. Alarm clock
The old watchmaker has a special digital alarm in its collection that rings whenever the sum of digits of the alarm is equal to 21. Find out when the alarm clock will ring. What is their number? List all options ...
16. 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 w
17. PIN - codes
How many five-digit PIN - code can we create using the even numbers?
18. 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?
19. 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?
20. Owner of the company
The owner of the company with extensive administrative activity wants to sell the obsolete 3 machines at the price of CZK 1000 per 1 machine with a six-month warranty period. If the machine breaks down during this period, the owner will return the employe

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