Permutations without repetition
The calculator calculates the number of permutations of n elements. Number of permutations is the number of ways to choose a sample of n elements from a set of n distinct objects where order does matter and repetition are not allowed. There are n! (n factorial) ways of arranging n objects into an ordered sequence.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
Permutations
The permutation is a synonymous name for a variation of the nth class of n-elements. It is thus any n-element ordered group formed of n-elements. The elements are not repeated and depend on the order of the elements in the group.P(n)=n(n−1)(n−2)...1=n!
A typical example is: We have 4 books, and in how many ways can we arrange them side by side on a shelf?
Foundation of combinatorics in word problems
- Seating
How many ways can 7 people sit on 5 numbered chairs (e.g., seat reservation on the train)? - Rectangles
How many rectangles with area 8855 cm² whose sides are natural numbers? - 7 heroes
6 heroes galloping on 6 horses behind. How many ways can we sort them behind? - Pairs
At the table sit 10 people, 5 on one side and 5 on the other side. Among them are 3 pairs. Every pair wants to sit opposite each other. How many ways can they sit?
- 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. - Hockey match
The hockey match ended with a result of 3:1. How many different storylines may the match have? - Dices throws
What is the probability that the two throws of the dice: a) Six falls even once b) Six will fall at least once
- Tokens
The non-transparent bags contain red, white, yellow, and blue tokens. We pulled one token three times and returned it again, writing down all possibilities. - VCP equation
Solve the following equation with variations, combinations, and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0 - Ružomberok 6070
The tourist group wanted to visit the four Slovak cities: Bratislava, Banská Bystrica, Ružomberok, and Levice. They decided that Levice would be the third place they would visit. How many different ways could they organize their city visit program? - Permutations 6450
Seven times the permutations of n elements equal one-eighth of the permutations of n + 2 elements. What is the number of elements? - Ribbons 6640
Danka knits a sweater and has a choice of seven colors. a) How many ways can he choose three colors for the sleeves? b) He wants ribbons of four colors on his back. How many options does he have to choose from?
How many three-digit numbers do we make from the numbers 4,5,6,7?more math problems »
