n choose k calculator n=10, k=7 result
Find out how many different ways you can choose k items from n items set without repetition and without order. This number is also called combination number or n choose k or binomial coefficient or simply combinations. See also general combinatorial calculator.Calculation:
Ck(n)=(kn)=k!(n−k)!n! n=10 k=7 C7(10)=(710)=7!(10−7)!10!=3⋅2⋅110⋅9⋅8=120
The number of combinations: 120
A bit of theory - the foundation of combinatorics
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?
Foundation of combinatorics in word problems
- Chess
How many ways can you select 4 fields on a classic chessboard with 64 fields so that fields don't have the same color? - Rectangles
How many rectangles with area 8855 cm² whose sides are natural numbers? - Pizza
A school survey found that 10 out of 15 students like pizza. If 5 students are chosen randomly, what is the probability that all 5 students like pizza? - Count of triangles
On each side of an ABCD square is 10 internal points. Determine the number of triangles with vertices at these points.
- Probabilities
If probabilities of A, B, and A ∩ B are P (A) = 0.62, P (B) = 0.78, and P (A ∩ B) = 0.26, calculate the following probability (of the union. intersect and opposite and its combinations): - Combinatorics
The city has 7 fountains. Works only 6. How many options are there that can squirt? - Chess
How many different ways can you initiate a game of chess (first pass)? - Three digits number
From the numbers 1, 2, 3, 4, and 5, create three-digit numbers whose digits do not repeat, and the number is divisible by 2. How many numbers are there? - Intersection of the lines
How many points do nine lines intersect in a plane, of which four are parallel, and of the other five, no two are parallel (and if we assume that only two lines pass through each intersection)?
- Medicine
We test medicine on six patients. For all, the drug doesn't work. If the drug success rate of 20%, what is the probability that medicine does not work? - Eight blocks
Dana had the task of saving the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be fo - Permutations without repetition
From how many elements can we create 720 permutations without repetition? - Two-digit 3456
Write all the two-digit numbers that can be composed of the digit 7,8,9 without repeating the digits. Which ones are divisible b) two, c) three d) six? - Points in plane
The plane is given 12 points, 5 of which are located on a straight line. How many different lines could be drawn from these points?
The five cards with the numbers 1, 2, 3, 4, and 5 put together all three-digit odd numbers. How many are there?more math problems »
