N Choose K Calculator n=10, k=5 result
Find out how many different ways you can choose k items from a set of n items 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=10 k=5 C5(10)=(510)=5!(10−5)!10!=5⋅4⋅3⋅2⋅110⋅9⋅8⋅7⋅6=252
The number of combinations: 252
A bit of theory - the foundation of combinatorics
Combinations
A combination of the 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 the order does not matter. In mathematics, such unordered groups are called sets and subsets. The count is called a combination number and is calculated as follows:Ck(n)=(kn)=k!(n−k)!n!
A typical example: we have 15 students and need to choose 3. How many ways can this be done?
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 6 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 all three-digit positive integers that can be formed from the digits 1, 2, 3, and 4, subject to the following conditions: the units digit is one of 1, 3, or 4, and the hundreds digit is 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 numbers
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 numbers
Create all four-digit numbers from digits 1,2,3,4,5, which can repeat. How many are there? - Number probability
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
more math problems »
