# 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:

$V_{k}(n)=n_{k}n=10k=4V_{4}(10)=10_{4}=10000$

### 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:$V_{k}(n)=n⋅n⋅n⋅n...n=n_{k}$

## Foundation of combinatorics in word problems

- N-gon

How many diagonals have convex 30-gon? - Football league

In the 5th football league is 10 teams. How many ways can be filled first, second, and third place? - Seating rules

In a class are 24 seats but in the 7.B class are only 18 students. How many ways can students sit? (The class has 12 benches. A bench is for a pair of students.) Result (large number) logarithm and thus write down as powers of 10. - 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? - Olympics

How many ways can six athletes be placed on the podium at the Olympics? Depend on the color of the metal. - Combinations of sweaters

I have four sweaters, two are white, one red and one green. How many ways can you sort it out? - Word MATEMATIKA

How many words can be created from the phrase MATEMATIKA by changing the letters' order, regardless of whether the words are meaningful? - Disembarked 5962

Twenty-two passengers boarded in Žilina. Everyone gradually disembarked on the Teplička, Strečno, Vrútky, and Martin lines (the wagon was already empty in Martin). How many ways could they come out?

- Seven

Seven friends agreed to send everyone a holiday card. How many postcards were sent? - A jackpot

How many times must I play this jackpot to win? A jackpot of seven games having (1 X 2), i.e., home win or away win. - Gertrude 62304

Six boys and six girls (among them Emil, Félix, Gertrude, and Hanka) want to dance. The number of ways they can make six (mixed) couples if Emil does not want to dance with Gertrude and Hanka wants to dance with Felix is? - Parking 72644

How many ways can ten cars park side by side in a parking lot? - Indistinguishable 74294

We have eight compartments where we put three indistinguishable balls and two distinguishable ones. How many options do we have?

more math problems »