n choose k calculator n=100, k=50 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=100 k=50 C50(100)=(50100)=50!(100−50)!100!≈1.008×1029=100891344545564193334812497256
The number of combinations: 1.0089134454556×1029
100891344545564193334812497256
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
- Party
At the party, everyone clinked with everyone. Together, they clink 406 times. How many people were at the party?
- Bits, bytes
Calculate how many different numbers can be encoded in a 16-bit binary word.
- Orchard
10 trees in 5 lines grow in the orchard. How many trees are in the orchard?
- Cards
How many ways can you give away 32 playing cards to 7 player?
- Trinity - triads
How many different triads can be selected from group 36 students?
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