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
- 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, there are 24 seats, but in the 7.B class, there 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? Depends on the color of the metal. - Combinations of sweaters
I have four sweaters: two white, one red, and one green. How many ways can you sort them 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?
Determine the number of all natural numbers greater than 200 in which the digits 1, 2, 4, 6, and 8 occur at most once each.more math problems »
