Permutations without repetition
The calculator calculates the number of permutations of n elements. Number of permutations is the number of ways to choose a sample of n elements from a set of n distinct objects where order does matter and repetition are not allowed. There are n! (n factorial) ways of arranging n objects into an ordered sequence.Calculation:
Vk(n)=(n−k)!n! n=10 k=4 V4(10)=(10−4)!10!=6!10!=10⋅9⋅8⋅7=5040
The number of variations: 5040
A bit of theory - the foundation of combinatorics
Permutations
The permutation is a synonymous name for a variation of the nth class of n-elements. It is thus any n-element ordered group formed of n-elements. The elements are not repeated and depend on the order of the elements in the group.P(n)=n(n−1)(n−2)...1=n!
A typical example is: We have 4 books, and in how many ways can we arrange them side by side on a shelf?
Foundation of combinatorics in word problems
- Subsets
How many are all subsets of set C = (97, 67, 66, 18, 59, 64)? - Neighborhood
I have 7 cups: 1 2 3 4 5 6 7. How many opportunities for standings cups are there if 1 and 2 are always neighborhood? - Eight blocks
Dana had the task of saving the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be fo - Combinations of sweaters
I have four sweaters: two white, one red, and one green. How many ways can you sort them out?
- Fourland 3542
In Fourland, they only have four letters F, O, U, and R, and every word has exactly four letters. No letter may be repeated in any word. Write all the words that can be written with them. - Competition
Fifteen boys and ten girls are in the class. In the school competition, a six-member team composed of four boys and two girls is selected. How many ways can we choose students? - Arrangements 4459
There are 4 classrooms on the ground floor of the school building, which are numbered 1,2,3,4. First-year students A, B, C, and D will be placed in these classrooms. Write all possible class arrangements and their number. Thank you - Find two digits
Find the possible values of A and B if the six-digit number 2A16B6 is divisible by 4 and 9. Please write the result as a composed number. - Ninth-grade 5446
When the ninth-grade boys and girls said goodbye at the end of the school year, they each gave each other their photos. It was a total of 552 images. How many farewells were there?
- Natural 5474
How many natural numbers can we create less than 301 from the number 0,1,2,3,6,7? - Tournament
Six teams entered the basketball tournament. How many matches will be played if each team has to play one match with the other? - Exactly 5803
There are 15 black and 20 white balls in Destiny. How many ways can six balls be drawn to have exactly two whites between them? - Dd 2-digit numbers
Find all odd 2-digit natural numbers compiled from digits 1; 3; 4; 6; and 8 if the digits are not repeated. - Identical 6517
The arranger is to display three identical beige, two identical green, and one black coat in the shop window. How many ways can it do that?
Five sticks with a length of 2,3,4,5,6 cm. How many ways can you choose three sticks to form three sides of a triangle?more math problems »
