Permutations - practice problems - page 8 of 18

Number of problems found: 342

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?
Seating pupils
We will work with a class in which there are 30 pupils, 40% of them are boys, the number of benches is 18. Determine the number of possibilities in the following tasks. 1) Determine in how many ways it is possible to select for a competition a trio of pup
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?
Permutations with repetitions
How many ways can the digits 1, 2, 2, 3, 3, 3, 4 be permuted into four-digit, three-digit, and two-digit numbers without repetition? Example: 4 digits: 1223, 2213, 3122, 2313, 4321, etc. 3 digits: 122, 212, 213, 432, etc. 2 digits: 12, 21, 31, 23 Note: I
Binary words
How many 10-bit words can be created with precisely four units (e.g., 1111000000)?
Route option
From Zubrohlava to Bobrov, there is one asphalt road, two forest roads, and one bike path. Find the number of ways we can get from Zubrohlava to Bobrov and back. List all options.
Syrups
In the shop, they sell three types of syrups - apple, raspberry, and orange. How many ways can you buy four bottles of syrup?
Odd number creation
How many odd three-digit numbers can you make of the five cards with the numbers 1, 2, 3, 5, and 6?
State name possibilities
If residents of MISSISSIPPI state have to use all the letters to choose their country's name, how many possibilities do they have?
Cups on the shelf
We should place two green, three red, and two yellow cups side by side on the shelf. a) How many different ways of setting up can arise? b) How many different ways of arranging can arise if cups of the same color stand side by side?
Book shelf arrangement
How many ways can we put seven different books on the shelf?
Team order possibilities
There are five good teams in the qualifying group for the World Cup. How many different orders can occur?
Medal division ways
Ten teams are playing in the Slovak hockey league. Gold, silver, and bronze medals are at stake. How many ways can it be divided?
Five-digit number creation
How many different five-digit numbers can we create from digits 4 and 5?
Seedbeds
The father wants to plant two seedbeds of carrots and two seedbeds of onion. Use a tree chart to find how many different options he has for placing the seedbeds.
Train wagon assembly
There are six tank cars, eight open and 12 closed wagons at the station. How many different trainsets can be assembled from them?
Sequentially pick
There are 6 different tickets marked with numbers 1 to 6 in the pocket. In how many different ways can we sequentially, taking into account the order, choose three of them, if the chosen tickets return to the pocket?

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