n choose k calculator n=1523, k=499 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

• 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%.
• Dice
  How many times must you throw the dice, and was the probability of throwing at least one päťky greater than 50%?
• Seating
  How many ways can 7 people sit on 5 numbered chairs (e.g., seat reservation on the train)?
• 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?
• 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?
• 2nd class variations
  From how many elements can you create 5112 variations of the second class?
• Chords
  How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?

• Guests
  How many ways can 8 guests sit down on 10 seats standing in a row?
• 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 16-bit binary word.
• Subsets
  How many 19 element subsets can be made from the 26 element set?
• Event probability
  The probability of event N in 5 independent experiments is 0.4. What is the probability that the event N occurs in one experiment (chance is the same)?

• Rectangles
  How many rectangles with area 8855 cm² whose sides are natural numbers?

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