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?
- Seating
How many ways can 7 people sit on 5 numbered chairs (e.g., seat reservation on the train)?
- Football league
In the 5th football league is 10 teams. How many ways can be filled first, second, and third place?
- Bits, bytes
Calculate how many different numbers can be encoded in a 16-bit binary word.
- Flags
How many different flags can be made from green, white, blue, red, orange, yellow, and purple materials, so each flag consists of three different colors?
- 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.
- Toys
3 children pulled 12 different toys from a box. How many ways can toys be divided so each child has at least one toy?
- No. of divisors
How many different divisors have number 13 4 * 2 4?
- Vans
In how many ways can 5 shuttle vans line up at the airport?
- 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?
- 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.
- 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?
- Seven-segmet
Lenka is amused that he punched a calculator (seven-segment display) number and used only digits 2 to 9. Some numbers have the property that She again gave their image in the axial or central symmetry some number. Determine the maximum number of three-dig
- A three-digit numbers
Determine the total number of positive three-digit numbers that contain a digit 7.
more math problems »