n choose k calculator n=111, k=10 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=111 k=10 C10(111)=(10111)=10!(111−10)!111!=51540966982791
The number of combinations: 51540966982791
51540966982791
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
- Probability - tickets
What is the probability when you have 25 tickets in 5000 that you do not win the first (one) prize?
- Family
What is the probability that a family with 3 children has: exactly 1 girl? 2 girls and 1 boys? Consider the birth probability of a girl as 48.66% and a boy as 51.34%.
- Phone numbers
How many 9-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated?
- Dice
How many times must you throw the dice, and was the probability of throwing at least one päťky greater than 50%?
- Lottery
The lottery is 60000 elk, in which 6200 wins. What is the probability that the purchase of 12 elks won nothing?
- N-gon
How many diagonals have convex 30-gon?
- Party
At the party, everyone clinked with everyone. Together, they clink 406 times. How many people were at the party?
- 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)
- Playing cards
How many possible ways are there to shuffle 8 playing cards?
- Chess
How many ways can you select 4 fields on a classic chessboard with 64 fields so that fields don't have the same color?
- Basketball
Peter and Franta threw to the basket. Each had 20 attempts. Peter scored thirteen and twelve Franta. Give them a percentage of success.
- 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.
- Area codes
How many 6 digit area codes are possible if the first number can't be zero?
more math problems »