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

• Examination
  The class is 25 students. How many ways can we choose 5 students for examination?
• Toys
  3 children pulled 12 different toys from a box. How many ways can toys be divided so each child has at least one toy?
• No. of divisors
  How many different divisors have number 13 ⁴ * 2 ⁴?
• Probabilities
  If probabilities of A, B, and A ∩ B are P (A) = 0.62, P (B) = 0.78, and P (A ∩ B) = 0.26, calculate the following probability (of the union. intersect and opposite and its combinations):

• Ace
  We pulled out one card from a complete set of playing cards (32 cards). What is the probability of pulling the ace?
• Hockey players
  After we cycle, five hockey players sit down. What is the probability that the two best scorers of this crew will sit next to each other?
• Bulb lifespan
  The probability that the bulb will burn for more than 800 hours is 0.2. There are 3 light bulbs in the hallway. What is the probability that after 800 hours, at least one will be lit?
• The confectionery
  The confectionery sold five kinds of ice cream. If the order of ice cream does not matter, how many ways can I buy three kinds?
• 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.

• Ten dices
  When you hit ten dice simultaneously, you get an average of 35. How much do you hit if every time you get six, you're throwing the dice again?
• Two-digit 3456
  Write all the two-digit numbers that can be composed of the digit 7,8,9 without repeating the digits. Which ones are divisible b) two, c) three d) six?
• Ice cream
  Annie likes ice cream. In the shop are six kinds of ice cream. How many ways can she buy ice cream in three scoops if each has a different flavor mound and the order of scoops doesn't matter?
• Distribution function
  X 2 3 4 P 0.35 0.35 0.3 The data in this table do I calculate the distribution function F(x) and then probability p(2.5 < ξ < 3.25) p(2.8 < ξ) and p(3.25 > ξ)
• Four-digit 3912
  Create all four-digit numbers from digits 1,2,3,4,5, which can repeat. How many are there?

• Probability 4020
  There are numbers from 1 to 20 in the hat. What is the probability that we will pull out from the hat: a / one-digit number b / prime number c / number greater than 11 d / a number divisible by six Thank you

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