Combinations without repetition
Find out how many different ways you can choose k items from n items set. With/without repetition, with/without order.Calculation:
Ck(n)=(kn)=k!(n−k)!n! n=11 k=3 C3(11)=(311)=3!(11−3)!11!=3⋅2⋅111⋅10⋅9=165
Number of combinations: 165
A bit of theory - 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, equivalent. For calculations, it is fully sufficient to use the procedure resulting from the combinatorial rule of product.
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?Variations with repetition
A variation of the k-th class of n elements is an ordered k-element group formed of a set of n elements, wherein the elements can be repeated and depends on their order. A typical example is the formation of numbers from the numbers 2,3,4,5, and finding their number. We calculate their number according to the combinatorial rule of the product: Vk′(n)=n⋅n⋅n⋅n...n=nkPermutations with repeat
A repeating permutation is an arranged k-element group of n-elements, with some elements repeating in a group. Repeating some (or all in a group) reduces the number of such repeating permutations. Pk1k2k3...km′(n)=k1!k2!k3!...km!n! A typical example is to find out how many seven-digit numbers formed from the numbers 2,2,2, 6,6,6,6.Combinations
A combination of a k-th class of n elements is an unordered k-element group formed from a set of n elements. The elements are not repeated, and it does not matter the order of the group's elements. In mathematics, disordered groups are called sets and subsets. Their number is a combination number and is calculated as follows: Ck(n)=(kn)=k!(n−k)!n! A typical example of combinations is that we have 15 students and we have to choose three. How many will there be?Combinations with repeat
Here we select k element groups from n elements, regardless of the order, and the elements can be repeated. k is logically greater than n (otherwise, we would get ordinary combinations). Their count is: Ck′(n)=(kn+k−1)=k!(n−1)!(n+k−1)! Explanation of the formula - the number of combinations with repetition is equal to the number of locations of n − 1 separators on n-1 + k places. A typical example is: we go to the store to buy 6 chocolates. They offer only 3 species. How many options do we have? k = 6, n = 3.Foundation of combinatorics in word problems
- PIN - codes
How many five-digit PIN - code can we create using the even numbers?
- Mastering
The student masters the subject matter for the exam in Czech to 98%, from Math to 86% and from Economics to 71%. What is the probability that he will fail from Math and from others will succeed?
- Intersection) 1566
How many points do 9 lines intersect in a plane, of which 4 are parallel to each other, and of the other 5 no two are parallel (and if we assume that only two lines pass through each intersection)?
- Arbitrary 69194
There are ten arbitrary points in the plane. How many circles can we make from them?
- MATES
In MATES (Small Television tipping), from 35 random numbers drawn 5 winning numbers. How many possible combinations are there?
- Six questions test
There are six questions in the test. There are three answers to each - only one is correct. To take the exam, students must answer at least four questions correctly. Alan didn't learn, so he circled the answers only by guessing. What is the probability th
- 7 heroes
9 heroes galloping on 9 horses behind. How many ways can sort them behind?
- Probability 3219
In recent years, it has rained 12 days in March. What is the probability that it rained on March 18?
- Three dice
The player throwing the three dice asked G. Galilei the question: "Should I bet on the sum of 11 or the sum of 12?" What did Galilei answer him? Hint: write down all three triples of numbers that can be thrown and: have a total of 11 have a total of 12 an
- Seven segments display
Electronic devices sometime make use of the type of digits below, where each digit uses a number of short stripes, for examples seven uses three small stripes. What is the largest three-digit number that you can make if you use twenty stripes?
- Equilateral 75284
Given are 6 line segments with lengths of 3 cm, 4 cm, 5 cm, 7 cm, 8 cm, and 9 cm. How many equilateral triangles can make from them? List all the options.
- The following
The following data represents the number of cases of coffee or filters sold by four sales reps in a recent sales competition. Sales Person; Gourmet; Single Cup; Filters; Total Connor; 142; 325; 30; 497 Paige ; 42; 125; 40; 207 Bryce ; 9; 100;
- Four digit codes
Given the digits 0-7. If repetition is not allowed, how many 4 digit codes that are greater than 2000 and divisible by 4, are possible?
- Blocks
There are nine interactive basic building blocks of an organization. How many two-blocks combinations are there?
- Chords
How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?
- Distribution function
X 2 3 4 P 0.35 0.35 0.3 The data in this table do I calculate the distribution function F(x) and then probability p(2.5 < ξ < 3.25) p(2.8 < ξ) and p(3.25 > ξ)
more math problems »