Reason + permutations - practice problems
Number of problems found: 110
- Five couples
In how many ways can 5 couples arrange themselves in a row if they stay together? - A ferry
A ferry with a capacity of 10 people takes a group of 13 men and 7 women across a river. Find the number of ways in which the group may be taken across the if all women go on the first group. - Kenneth 2
Kenneth has 100 pennies, 20 nickels, 10 dimes, and 4 quarters. How many ways can he choose coins that total 25 cents? - Probability 82744
Ten books are placed randomly on one shelf. Find the probability that certain three books are placed next to each other. - Permutations 82516
From how many elements can we make 5040 permutations without repetition? - Different 82447
How many 4 colored flags can be made from 5 colors so that each flag consists of three different colors? - Possibilities 82372
A hockey match played for three periods ended with a score of 2:3. How many possibilities are there on how the given thirds could have been completed? - 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? - Four-digit 82023
How many four-digit numbers are there in which there are at least three eights - 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: - Position 81987
Find a number with six digits. If you put the last digit before the first, you get a new number that is five times larger. The digits between must not change their position. - Probability 81679
What is the probability that a roll of three dice will result in a number less than 7? - 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. - Positive integer integral
How many different sets of a positive integer in the form (x, y, z) satisfy the equation xyz=1400? - 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 - Completely 79274
Kitchen cabinets are sold in widths of 80 cm, 60 cm, and 40 cm. Which assembly can we choose if we have a wall 3.5 m long and we want to completely fill it with an assembly that also includes a dishwasher, the width of which is 60 cm, and the stove is 50 - Socks
Ben's favorite colors are blue and green. He has six blue socks and six green socks in his sock drawer. Unfortunately, they are completely mixed up, and one day, he has to grab some socks to wear in complete darkness. How many socks (minimum) does he have - Non equivalent ints
Two n-digit integers are said to be equivalent if one is a permutation of the other. Find the number of 5-digit integers such no two are equivalent. If the digit 5,7,9 can appear at most one, how many non-equivalent five-digit integers are there? - Equilateral 75284
Given are 6 line segments with lengths of 3 cm, 4 cm, 5 cm, 7 cm, 8 cm, and 9 cm. How many equilateral triangles can make from them? List all the options.
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