K-permutations - practice problems - page 3 of 15

Number of problems found: 292

Flag color combinations
How many 4 colored flags can be made from 5 colors so that each flag consists of three different colors?
Play match
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?
Ball selection choices
There are 15 black and 15 white balls in an opaque bag. Elenka took one ball out of the bag three times. what choices of the three balls could she choose?
Dance party
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 eight count
How many four-digit numbers are there in which there are at least three eights
Monogram letter combinations
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 of digits
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.
Aquaristics
We consider 'words' (i.e., arbitrary strings of letters) obtained by rearranging the letters of the word 'AQUARISTICS'. All letters are treated as distinguishable from each other. The number of such words that also contain the string 'CAVA' (as consecutiv
Volleyball tournament teams
The school volleyball tournament was played on a one-on-one basis. One match lasted 15 minutes, and 3 hours and 45 minutes were played. Calculate how many teams participated.
Dice sum probability
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)?
Cube tower ways
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 cubes are indistinguishable, and so are blue cubes.
Lottery ticket probability
In the lottery, where 326 numbers are drawn, Maros marked 7 numbers on the ticket. Kevin marked 11 numbers in another lottery, and 421 numbers were drawn. Which of these friends has a better chance of winning?
Positive integer integral
How many different sets of a positive integer in the form (x, y, z) satisfy the equation xyz=1400?
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.
Dance pair duration
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
Kitchen cabinet assembly
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?
A fair coin
A fair coin is tossed twice. Write down the set of possible outcomes. What is the probability of obtaining it? I. Exactly one head ii. No head

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