Variations with repetition
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:
Vk′(n)=nk n=10 k=4 V4′(10)=104=10000
The number of variations with repetition: 10000
A bit of theory - the foundation of combinatorics
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:Vk′(n)=n⋅n⋅n⋅n...n=nk
Foundation of combinatorics in word problems
- Playmakers 83340
In a basketball game, two pivots, two wings, and one point guard play. The coach has three pivots, four wing players, and two playmakers available on the bench. How many different five players can a coach send to the board during a game? - Variations
Find the number of items when the count of variations of the fourth class without repeating is 42 times larger than the count of variations of the third class without repetition. - Choices 82334
There are 15 black and 15 white balls in an opaque bag. Elenka took one ball out of the bag three times. what choices of the three balls could she choose? - Three coins
In a game of chance where three coins are tossed, a player wins if two heads and a tail come up. What are the chances of this occurring?
- Disco
At the disco goes 12 boys and 15 girls. In how many ways can we select four dancing couples? - Tournament
Six teams entered the basketball tournament. How many matches will be played if each team has to play one match with the other? - Election 4
In a certain election, there are three presidential candidates: 5 for secretory and 2 for treasurer. Find how many ways the election may (turn out/be held). - Variation equation
Solve combinatorics equation: V(2, x+8)=72 V(2,x+8) is variations, second class, from x+8 items. - Competition 69474
There are ten girls and seven boys in the dance group. Only one mixed couple is to go to the competition. How many are all possible pairs from which we can choose a pair for the competition?
- Options 3572
We roll three dice. Write down all the feast options. - Metals
In the Hockey World Cup, play eight teams, and determine how many ways they can win gold, silver, and bronze medals. - T-shirts 73074
Dušan has 8 T-shirts and three pairs of shorts in his closet. How many ways can he dress for school? - Three-part novel
In how many ways can seven books be stored on a shelf if there is one three-part novel to be placed side by side? - Friends 81380
In the lottery, where 326 numbers are drawn, Maros marked 7 numbers on the ticket. Kamil marked 11 numbers in another lottery, and 421 numbers were drawn. Which of these friends has a better chance of winning?
more math problems »