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
- Trinity
How many different triads can be selected from group 38 students? - Designated 66594
Marenka is required to read three books out of five designated books. How many ways can three books choose to be read? - Calculation of CN
Calculate: (486 choose 159) - (486 choose 327) - Different 68754
We have six balls of different colors. We select two balls at once. How many options?
- Pet store 2
A pet store is having a prize giveaway. The spinner shows the type of toy a customer can win for their pet. If a customer spins the spinner and it lands on a cat, they will win a free cat toy. If the spinner is spun 540 times throughout the day, about how - Playmakers 83340
In a basketball game, two pivots, two wings, and one point guard play. The coach has three pivots, four wing players, and two playmakers available on the bench. How many different five players can a coach send to the board during a game? - Chords
How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones? - The six
The six boys will be led up the hill by a two-seater lift. How many options are there? - Cards
The player gets eight cards of 32. What is the probability that it gets a) all four aces b) at least one ace
- Student examination
How many ways can a teacher select a group of 6 students to sit in the front row if the class has 13 students? - Soccer teams
Have to organize soccer teams. There are three age groups. How many different ways can you organize ten teams for each age group? Is this a permutation or combination? - How many 31
How many ways can a teacher select a group of 3 students to sit in the front row if the class has 13 students? - Three digits number 2
Find the number of all three-digit positive integers that can be put together from digits 1,2,3,4 and which are subject to the same time has the following conditions: on one position is one of the numbers 1,3,4, on the place of hundreds 4 or 2. - Chocolates 38751
Jane wants to buy six chocolates in the store. The store offers only three species of chocolates. How many options does she have?
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