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
- Metals
In the Hockey World Cup, play eight teams, and determine how many ways they can win gold, silver, and bronze medals. - Peak
Uphill leads 2 paths and one lift. a) How many options back and forth are there? b) How many options to get there and back by the not same path are there? c) How many options back and forth are there that we go at least once a lift? - Seven
Seven friends agreed to send everyone a holiday card. How many postcards were sent? - 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? - A basket 4
A basket contains 9 fruits, where 4 are oranges, and the rest are mangoes. Three fruits are taken out one at a time and put aside. Find the probability that 3 are oranges. - Hockey players
After we cycle, five hockey players sit down. What is the probability that the two best scorers of this crew will sit next to each other? - Chocolates
How many ways can we distribute eight different chocolates to four children? - Dices throws
What is the probability that the two throws of the dice: a) Six falls even once b) Six will fall at least once - Alarm clock
The old watchmaker has a unique digital alarm in its collection that rings whenever the sum of the alarm's digits equals 21. Find out when the alarm clock will ring. What is their number? List all options. - Chess
How many ways can you select 4 fields on a classic chessboard with 64 fields so that fields don't have the same color? - Syrups
In the shop, they sell three types of syrups - apple, raspberry, and orange. How many ways can you buy four bottles of syrup? - Five letters
How many ways can five letters be arranged? - Tic-tac-toe
In how many ways could 9 participants of the school round of five-in-a-row win the first three places? - Indistinguishable 81481
How many ways can a tower of five yellow and four blue cubes be built so that each yellow cube is adjacent to at least one other yellow cube? Yellow dice are indistinguishable, and so are blue dice. - How many 4
How many four-digit numbers that are divisible by ten can be created from the numbers 3, 5, 7, 8, 9, and 0 such no digits repeats?
more math problems »