Variations - practice problems - page 3 of 16
Number of problems found: 313
- Aquaristics
We consider “words” (i.e. arbitrary strings of letters) obtained by rearranging the letters of the word “AQUARISTICS”. All letters are distinguishable from each other here. The number of such words that also contain the expression “CAVA” (as consecutive l - Consecutively numbers
How many ways are there to arrange the numbers 3, 2, 15, 8, and 6 so that the even numbers are arranged in ascending order (not necessarily consecutively)? - 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
Find the number of all natural numbers greater than 200 in which the digits 1, 2, 4, 6, 8 occur at most once and not contains any other digits. - Different 79704
Thirty-two boys and 34 girls came to the dance. How many different dance pairs can they make, given that each team is given: they can only dance for 1 minute and then take turns in 5 seconds? Calculate how long the dance evening would last for all the pai - Four digit codes
Given the digits 0-7. If repetition is not allowed, how many four-digit codes greater than 2000 and divisible by 4 are possible? - Indistinguishable 74294
We have eight compartments where we put three indistinguishable balls and two distinguishable ones. How many options do we have? - 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? - Probability 72324
When entering the PIN code, we used the digits 2, 3, 4, 5, and 7 only once. What is the probability that someone will guess our PIN code on the first try? - 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?
- Variations 70724
If we increase the number of elements by 2, the number of variations of the second class without repetition increases by 22. How many elements do we have initially? - Assemble 70414
How many ways can we assemble five wagons when sand is in three wagons and cement in two? - 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 - Together 70124
Twins Ela and Nela came to the cinema together with their friend Hela. Only the first 10 seats in the third row are free. How many ways can they be seated if the twins want to sit next to each other, with Nela always to Ela's left and Hel right next to on - Altogether 69994
Twelve players signed up for the squash tournament. Based on the lottery, they formed pairs, and in the first round, each pair played one match. The winners advanced to the second round, where they played each other one game at a time. How many matches we
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