n choose k calculator n=300, k=2 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=300 k=2 C2(300)=(2300)=2!(300−2)!300!=2⋅1300⋅299=44850
The number of combinations: 44850
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
- Rectangles
How many rectangles with area 8855 cm² whose sides are natural numbers? - 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): - 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)? - 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? - Three-digit code
The five cards with the numbers 1, 2, 3, 4, and 5 put together all three-digit odd numbers. How many are there? - Page numbering
The book has 88 pages. How many times is the number 4 used for the book numbering? - Six on dice
When throwing two dice, what is the probability they will fall at least one six? - Divisible 5454
How many natural numbers are divisible by five less than 8000, composed of the digits 0,1,2,5,7,9? - Four-digit 65124
Please find out how many different four-digit numbers we can create from the digits 3 and 8 so that the two digits three and two digits eight are used in each four-digit number created. - Gradually 67284
Petra borrowed four books from the library at the beginning of the summer holidays. How many orders in which she could gradually read them? - Three-digit 67824
The numbers 1,3,7,4 are given. How many three-digit numbers are there: a) if the numbers can be repeated b) if the numbers cannot be repeated c) how many even three-digit numbers if the numbers can be repeated d) how many odd three-digit numbers if the nu - Probability 69714
The factory produces 35% of the tiles on line A, which produces scrap with a probability of 0.02, and 65% on line B, where the probability of scrap is 0.03. What is the probability that the selected tile will be defective? - Different 79704
Thirty-two boys and 34 girls came to the dance. How many different dance pairs can they make, given that each team is given: they can only dance for 1 minute and then take turns in 5 seconds? Calculate how long the dance evening would last for all the pai - Different balls
We have four different boxes and three identical balls. Place the marbles in these boxes so that the boxes can contain one, two, three or none. How many other locations are there?
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