Permutations without repetition n=11, k=11 resultThe 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.
P(n)=n! n=11 P(11)=11!=39916800
The number of permutations: 39916800
A bit of theory - the foundation of combinatorics
VariationsA variation of the k-th class of n elements is an ordered k-element group formed from a set of n elements. The elements are not repeated and depend on the order of the group's elements (therefore arranged).
The number of variations can be easily calculated using the combinatorial rule of product. For example, if we have the set n = 5 numbers 1,2,3,4,5, and we have to make third-class variations, their V3 (5) = 5 * 4 * 3 = 60.
n! we call the factorial of the number n, which is the product of the first n natural numbers. The notation with the factorial is only clearer and equivalent. For calculations, it is fully sufficient to use the procedure resulting from the combinatorial rule of product.
PermutationsThe 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.
A typical example is: We have 4 books, and in how many ways can we arrange them side by side on a shelf?
Variations with repetitionA variation of the k-th class of n elements is an ordered k-element group formed of a set of n elements, wherein the elements can be repeated and depends on their order. A typical example is the formation of numbers from the numbers 2,3,4,5, and finding their number. We calculate their number according to the combinatorial rule of the product:
Permutations with repeatA repeating permutation is an arranged k-element group of n-elements, with some elements repeating in a group. Repeating some (or all in a group) reduces the number of such repeating permutations.
A typical example is to find out how many seven-digit numbers formed from the numbers 2,2,2, 6,6,6,6.
CombinationsA combination of a k-th class of n elements is an unordered k-element group formed from a set of n elements. The elements are not repeated, and it does not matter the order of the group's elements. In mathematics, disordered groups are called sets and subsets. Their number is a combination number and is calculated as follows:
A typical example of combinations is that we have 15 students and we have to choose three. How many will there be?
Combinations with repeatHere we select k element groups from n elements, regardless of the order, and the elements can be repeated. k is logically greater than n (otherwise, we would get ordinary combinations). Their count is:
Explanation of the formula - the number of combinations with repetition is equal to the number of locations of n − 1 separators on n-1 + k places. A typical example is: we go to the store to buy 6 chocolates. They offer only 3 species. How many options do we have? k = 6, n = 3.
Foundation of combinatorics in word problems
How many different triads can be selected from group 38 students?
- Opportunities 8372
There are 20 students in the class, four of them are being tested by the teacher. How many options are there to choose who the teacher will test?
At the disco goes 12 boys and 15 girls. In how many ways can we select four dancing couples?
- School parliament
There are 18 boys and 14 girls in the class. In how many ways can three representatives be elected to the school parliament if these are to be: a) the boys themselves b) one boy and two girls
- Possibilities 81788
The ring consists of 4 beads. There are 5 different colors of beads in the package. How many possibilities are there to create one ring, and can the colors repeat?
How many ways can you give away 32 playing cards to 7 player?
10 trees in 5 lines grow in the orchard. How many trees are in the orchard?
- Distribution 2645
The worker operates 600 spindles on which the yarn is wound. The probability of tearing the yarn on each spindle at time t is 0.005. a) Determine the probability distribution of the number of torn spindles at time t and the mean and variance. b) What is t
- travel agency
A small travel agency offers five different tours on honeymoon. What is the probability that the bride and groom choose the same tour (they choose independently)?
- 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.
- Numbers 72404
How many numbers are less than 200, the digits sum of which is 6?
- Positions 26151
How many positions are there to store three books on the shelf?
- Repetition 80362
How many six-digit numbers without repetition can be formed from the digits 1, 2, 3, 4, 5, and 6, if the numbers are, to begin with: a) the digit 4; b) digits 4 or 5?
Ruben owns a restaurant. He likes to keep track of everything customers are buying. His top 3 sellers are sandwiches, salads, and pizza. He knows that 1/3 of his customers buy a sandwich, 1/2 buy a salad, and 1/4 buy a pizza. What fraction of customers bu
- Gold, silver, bronze
How many ways can we divide gold, silver, and bronze medals if six people compete?
more math problems »