Variations - practice for 13 year olds
Number of problems found: 103
- The marathon
There are 12 athletes joining the Topolcany Marathon Event. How many ways can the first, second, and third placers be chosen? - A bag 6
A bag contains 3 red marbles, 8 blue marbles, and 5 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that both marbles drawn will be blue? - Married 83309
In how many ways can we seat five guests at a table, two of whom are married and want to sit next to each other? - Different 82447
How many 4 colored flags can be made from 5 colors so that each flag consists of three different colors?
- Discovered 82210
At the dance party, the organizer discovered that 168 different dance pairs could be formed from girls and boys. How many boys are there at the dance if there are 12 girls? - Repetition: 82003
Calculate how many different monograms (short name and surname) I can make from the letters A, E, M, Z, and K. a) with repetition: b) without repetition: - Indistinguishable 81481
How many ways can a tower of five yellow and four blue cubes be built so that each yellow cube is adjacent to at least one other yellow cube? Yellow dice are indistinguishable, and so are blue dice. - Friends 81380
In the lottery, where 326 numbers are drawn, Maros marked 7 numbers on the ticket. Kamil marked 11 numbers in another lottery, and 421 numbers were drawn. Which of these friends has a better chance of winning? - Natural numbers
Determine the number of all natural numbers greater than 200 in which the digits 1, 2, 4, 6, and 8 occur at most once each.
- Four numbers
I am a four-digit number, no zeros, in which the first number is five times the last, the second is four more than the first and three times the third, and the third is two more than the last and two less than the first. - Four-digit 73114
How many four-digit numbers can we assemble from the digits 2, 6, 3, 5, 1, and 9 if the numerals in the number cannot be repeated? - T-shirts 73074
Dušan has 8 T-shirts and three pairs of shorts in his closet. How many ways can he dress for school? - Parking 72644
How many ways can ten cars park side by side in a parking lot? - Groups 72194
I have eight groups. How could they place first, second, and third?
- Three-digit 72184
How many three-digit numbers can be created from the numbers 1, 2, 3, and 4 if you can repeat them? - Distribute 70244
We have to distribute the keys to the safe among four people so that no two of them can open the safe but in such a way that any three can open the safe. How many minimum keys do we need? How to divide them? How many minimum locks must be on the safe? All - Classical 69634
Peter, Jano, Alice, and Rebecca attended a classical concert. How many different ways can they sit in the four free seats if Rebecca wants to sit with John? - Michalovci 69494
How many different courses could the match between AC Michalovci and Juvent Turiec have, which ended 2:1? - Competition 69474
There are ten girls and seven boys in the dance group. Only one mixed couple is to go to the competition. How many are all possible pairs from which we can choose a pair for the competition?
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