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.

Elements to choose from:

(n)

Elements chosen:

(k)

Calculate

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:

$C_k(n)=\left(\genfrac{}{}{0ex}{}{n}{k}\right)=\frac{n!}{k!(n-k)!}$

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?

• 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.

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