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
- Seven
Seven friends agreed to send everyone a holiday card. How many postcards were sent? - Parking 72644
How many ways can ten cars park side by side in a parking lot? - 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? - Football league
In the 5th football league is 10 teams. How many ways can be filled first, second, and third place?
- 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. - Natural numbers
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. - Olympics
How many ways can six athletes be placed on the podium at the Olympics? Depend on the color of the metal. - Word MATEMATIKA
How many words can be created from the phrase MATEMATIKA by changing the letters' order, regardless of whether the words are meaningful? - 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.
- N-gon
How many diagonals have convex 30-gon? - 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? - Indistinguishable 74294
We have eight compartments where we put three indistinguishable balls and two distinguishable ones. How many options do we have? - Combinations of sweaters
I have four sweaters, two are white, one red and one green. How many ways can you sort it out? - Morse alphabet
Calculate how many words of Morse code to create compiling dashes and dots in the words of one to four characters.
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