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
- 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?
- 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?
- 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
- Metals
Play eight teams in the Hockey World Cup and determine how many ways they can win gold, silver, and bronze medals.
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How many attempts do I need to guess the 3-digit PIN to be sure I can guess it?
- 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.
- Seven
Seven friends agreed to send everyone a holiday card. How many postcards were sent?
- Ribbons 6640
Danka knits a sweater and has a choice of seven colors. a) How many ways can he choose three colors for the sleeves? b) He wants ribbons of four colors on his back. How many options does he have to choose from?
- Certificate 6740
There are 19 children in class 6A, 7 subjects, and no one has a worse grade than a three. Can each of them have a different certificate? How many would have to be in the class so that everyone could not have another report card?
- Chocolates
How many ways can we distribute eight different chocolates to four children?
- 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.
- 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?
- 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?
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