Combinations Calculator
The calculator finds the number of combinations of the k-th class from n elements without repetition. A combination without repetition of k objects from n is a way of selecting k objects from a list of n. The order of selection does not matter and each object can be selected once (without repetition).Calculation:
Ck(n)=(kn)=k!(n−k)!n! n=10 k=4 C4(10)=(410)=4!(10−4)!10!=4⋅3⋅2⋅110⋅9⋅8⋅7=210
The number of combinations: 210
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
- Combinatorial examples
1. In the class you have 15 pupils. In how many ways can we select four for examination? 2. In how many ways can we select from seven-card cards (32 cards) any two cards? 3. In how many ways can we divide 12 pupils into two six-member teams? 4. In how man - Numbered
In the past, passengers on public transport validated single-use tickets that had 9 numbered boxes, a certain number of which were punched with a validator. A) In how many different ways could a ticket be validated if 3 boxes were punched? B) In how many - Book selection ways
Mary is required to read three books out of five designated books. How many ways can three books choose to be read? - In the shipment
There are 40 products in a shipment, of which 4 are defective. In how many ways can 5 products be selected so that exactly 3 of them are non-defective? - Population variance
60% of students at a California community college will transfer to a college in the CSU system. The number of students in a sample who will transfer follows a binomial distribution. If eight students are randomly selected, find the population variance σ²
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