# Variations with repetition n=49, k=5 result

The calculator calculates the number of variations with repetition. A variation of the k-th class with repetition of n elements is any ordered k-element group composed of only these n elements such that each element can be repeated any number of times.## Calculation:

$V_{k}(n)=n_{k}n=49k=5V_{5}(49)=49_{5}=282475249$

### The number of variations with repetition: 282475249

282475249

# A bit of theory - the foundation of combinatorics

## Variations

A 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 V

_{3}(5) = 5 * 4 * 3 = 60.

$V_{k}(n)=n(n−1)(n−2)...(n−k+1)=(n−k)!n! $

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.

## 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?

## Variations with repetition

A 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:$V_{k}(n)=n⋅n⋅n⋅n...n=n_{k}$

## Permutations with repeat

A 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.$P_{k_{1}k_{2}k_{3}...k_{m}}(n)=k_{1}!k_{2}!k_{3}!...k_{m}!n! $

A typical example is to find out how many seven-digit numbers formed from the numbers 2,2,2, 6,6,6,6.

## Combinations

A 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:$C_{k}(n)=(kn )=k!(n−k)!n! $

A typical example of combinations is that we have 15 students and we have to choose three. How many will there be?

## Combinations with repeat

Here 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:$C_{k}(n)=(kn+k−1 )=k!(n−1)!(n+k−1)! $

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

- Trinity

How many different triads can be selected from group 38 students? - Designated 66594

Marenka is required to read three books out of five designated books. How many ways can three books choose to be read? - Calculation of CN

Calculate: (486 choose 159) - (486 choose 327) - Pet store 2

A pet store is having a prize giveaway. The spinner shows the type of toy a customer can win for their pet. If a customer spins the spinner and it lands on a cat, they will win a free cat toy. If the spinner is spun 540 times throughout the day, about how - Chords

How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones? - The six

The six boys will be led up the hill by a two-seater lift. How many options are there? - Cards

The player gets eight cards of 32. What is the probability that it gets a) all four aces b) at least one ace - Soccer teams

Have to organize soccer teams. There are three age groups. How many different ways can you organize ten teams for each age group? Is this a permutation or combination? - How many 32

How many ways can a teacher select a group of 6 students to sit in the front row if the class has 13 students? - How many 31

How many ways can a teacher select a group of 3 students to sit in the front row if the class has 13 students? - Different 68754

We have six balls of different colors. We select two balls at once. How many options? - Lottery

Fernando has two lottery tickets, each from the other lottery. In the first is 973 000 lottery tickets from them wins 687 000, the second has 1425 000 lottery tickets from them wins 1425 000 tickets. What is the probability that at least one Fernando's ti - Distribution function

X 2 3 4 P 0.35 0.35 0.3 The data in this table do I calculate the distribution function F(x) and then probability p(2.5 < ξ < 3.25) p(2.8 < ξ) and p(3.25 > ξ) - Permutations without repetition

From how many elements can we create 720 permutations without repetition? - Combinations

From how many elements can we create 990 combinations, 2nd class, without repeating?

more math problems »