n choose k calculator n=5, k=1 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?
• Dice
  How many times must you throw the dice, and was the probability of throwing at least one pětky greater than 70%?
• N-gon
  How many diagonals have convex 30-gon?
• 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)
• Basketball
  Peter and Franta threw to the basket. Each had 20 attempts. Peter scored thirteen and twelve Franta. Give them a percentage of success.
• 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.

• Football league
  In the 5. football league is 10 teams. How many ways can be filled first, second, and third place?
• 2nd class combinations
  From how many elements can you create 2346 combinations of the second class?
• Confectionery
  The village markets have 5 kinds of sweets. One weighs 31 grams. How many different ways can a customer buy 1.519 kg sweets?
• Tournament
  Determine how many ways can be chosen two representatives from 34 students to school tournament.
• 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?
• Flags
  How many different flags can be made from green, white, blue, red, orange, yellow, and purple materials, so each flag consists of three different colors?

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