K-permutations - practice problems - page 7 of 15
Number of problems found: 292
- Round table
Find the number of ways in which eight people can be seated at a round table such that 2 of them always sit together. - Balls in row
Calculate the number of ways of placing four black balls, four turquoise balls, and five gold balls in a row. - Hockey podium possibilities
How many different positions can there be in the first three places in the hockey world championship if 12 teams are playing in them? How many possibilities exist if we are only concerned with which teams will be on the podium? - Family trip
Dulikovci, Elikovci, Filikovci, and Galikovci visited each other often last month. Each family visited each family exactly once. How many visits did all four families make together? If two families came to visit one family simultaneously, count it twice. - Nine-digit numbers
Determine the number of nine-digit numbers in which each of the digits 0 through 9 occurs at most once and in which the sums of the digits 1 through 3, 3 through 5, 5 through 7, and 7 to the 9th place are always equal to 10. Find the smallest and largest - The flag
The flag should consist of 3 different-colored stripes—available colors are white, red, blue, green, and yellow. Specify: A) number of all flags B) number of flags with a blue stripe C) number of flags with a blue stripe in the middle D) the number of fla - Covid-19 spread
A Street has 13 houses in a row. Some residents in the first house tested positive for Covid-19. The virus spreads in 2 ways: It can spread to the next house or jump directly to the third house. Residents of house two can get infected in only one way, hou - Five number code
I forgot a five-digit code on the bag. I remember that it was a symmetric number, and the sum of its digits was 22. Write down all the numbers that can be coded. - Hockey Championships
At the 2021 World Hockey Championships, there are eight teams in Group A, each playing seven matches. There are 4 points for each team to gain points (3-2-1-0), but it is always paired with the opponent's points ( 0-1-2-3). How many points are there possi - Tower board placement
How many ways can we build eight indistinguishable towers on an 8 × 8 board so they don't endanger each other? - A married
A married couple planned to have three children. i. List the possible combinations of the sexes of 3 children. Use B for a boy and G for a girl. ii. Calculate the probability that all three children would be of the same gender - Combinations
Evaluate the following expression involving combinations and permutations: C(6,3) + 3 P(6,3) - How many 13
How many ways can X³ y⁴ z³ be written without an exponent? - A department
There are seven women and five men in a department. a) how many ways can a committee of 3 people be selected? b) how many ways can a committee of 2 men and one woman be selected? c) how many ways can a committee of at least two women be selected (3 people - Three wagons
I have six different people (A, B, C, D, E, F), which I have to place into three wagons if it depends on who will board. How many options are there? - Tic-tac-toe
In how many ways could 9 participants of the school round of five-in-a-row win the first three places? - Permutation exclusion problem
I want to find the number of permutations of the set M6 if not one element is in that position as in the original input (1 2 3 4 5 6). So I have to exclude numbers with 1 in 1st place, 2 in 2nd place, and 3 in 3rd place. - Natural number creation How many natural numbers can you make from the digits contained in the number 4002? No digit may be repeated in the number entry. However, not all digits must be used. Sort the numbers in ascending order of size.
- Book reading ways
Martina borrowed three novels and two travelogues from the library. He will read the travelogues first. How many ways can he read the books? - Fruits
We want to plant five fruit trees in the garden, of which three are apple trees and two pears. How many different ways can we organize them?
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