Variations without repetition
The calculator calculates the number of variations of the k-th class from n elements. Variation is a way of selecting k items from a collection of n items (k ≤ n), such that (like permutations) the order of selection does matter. The repetition of items is not allowed.Calculation:
Vk(n)=(n−k)!n! n=10 k=4 V4(10)=(10−4)!10!=6!10!=10⋅9⋅8⋅7=5040
The number of variations: 5040
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 V3 (5) = 5 * 4 * 3 = 60.
Vk(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.
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? - 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? - 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? - 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.
- Tournament
Six teams entered the basketball tournament. How many matches will be played if each team has to play one match with the other? - T-shirts 73074
Dušan has 8 T-shirts and three pairs of shorts in his closet. How many ways can he dress for school? - 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. - Four-digit 65124
Please find out how many different four-digit numbers we can create from the digits 3 and 8 so that the two digits three and two digits eight are used in each four-digit number created.
more math problems »