N Choose K Calculator n=72, k=10 result
Find out how many different ways you can choose k items from a set of n items 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:
The number of elements (n) must not be less than the number of selected elements (k). If n < k, the calculation proceeds with the values of n and k swapped.
Ck(n)=(kn)=k!(n−k)!n! n=72 k=10 C10(72)=(1072)=10!(72−10)!72!=536211932256
The number of combinations: 536211932256
536211932256
A bit of theory - the foundation of combinatorics
Combinations
A combination of the 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 the order does not matter. In mathematics, such unordered groups are called sets and subsets. The count is called a combination number and is calculated as follows:Ck(n)=(kn)=k!(n−k)!n!
A typical example: we have 15 students and need to choose 3. How many ways can this be done?
Foundation of combinatorics in word problems
- Probability - tickets
What is the probability when you have 25 tickets in 5000 that you do not win the first (one) prize? - Dice
How many times must you throw the dice, and was the probability of throwing at least one pětky greater than 70%? - N-gon
How many diagonals does a convex 30-gon have? - Seating
How many ways can 7 people sit on 5 numbered chairs (e.g., seat reservation on the train)? - School trip
The class has 19 students. How can students be accommodated in the hostel, where available 3× 2-bed, 3× 3-bed and 1× 4-bed rooms? (Each room has its unique number) - Basketball
Peter and Frank shot baskets. Each had 20 attempts. Peter scored thirteen and Frank scored twelve. Calculate each one's success rate as a percentage. - Insurance
The house owner is insured against natural disasters and pays 0.05% annually of the value of the house 88 Eur. Calculate the value of the house. Calculate the probability of disaster if you know that 50% of the insurance is to pay damages. - Football league
In the 5. football league is 10 teams. How many ways can be filled first, second, and third place? - 2nd class combinations
From how many elements can you create 2346 combinations of the second class? - Confectionery
The village markets have 7 kinds of sweets. One weighs 37 grams. How many different ways can a customer buy 2.257 kg sweets? - Tournament
Determine how many ways can be chosen štyria representatives from 32 students to school tournament. - Examination
The class is 25 students. How many ways can we choose 5 students for examination? - Bits, bytes
Calculate how many different numbers can be encoded in a 64-bit binary word. - Subsets
How many 19 element subsets can be made from the 26 element set? - Flags
How many different flags can be made from green, white, blue, red, orange, yellow, and purple materials if each flag consists of three stripes of different colours?
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