n choose k calculator n=7, k=3 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=7 k=3 C3(7)=(37)=3!(7−3)!7!=3⋅2⋅17⋅6⋅5=35
The number of combinations: 35
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
- Two doctors
Doctor A will determine the correct diagnosis with a probability of 89% and doctor B with a probability of 75%. Calculate the probability of proper diagnosis if both doctors diagnose the patient. - Examination
The class is 25 students. How many ways can we choose 5 students for examination? - Lines
How many points will intersect 27 different lines where no two are parallel? - Pediatrician
Pediatrician, this month of 20 working days takes 4 days holidays. What is the probability that it will be at work on Monday?
We have 5 bags. Each consists of one green and 2 red balls. From each, we pull just one ball. What is the probability that we don't pull any green ball?more math problems »
