Combinations calculator
The calculator finds the number of combinations of the k-th class from n elements without repetition. A combination with 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 repeated).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 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:Ck(n)=(kn)=k!(n−k)!n!
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
- Trinity
How many different triads can be selected from group 38 students? - Opportunities 8372
There are 20 students in the class, four of them are being tested by the teacher. How many options are there to choose who the teacher will test? - School parliament
There are 18 boys and 14 girls in the class. In how many ways can three representatives be elected to the school parliament if these are to be: a) the boys themselves b) one boy and two girls - Disco
At the disco goes 12 boys and 15 girls. In how many ways can we select four dancing couples?
- Cards
How many ways can you give away 32 playing cards to 7 player? - Possibilities 81788
The ring consists of 4 beads. There are 5 different colors of beads in the package. How many possibilities are there to create one ring, and can the colors repeat? - travel agency
A small travel agency offers five different tours on honeymoon. What is the probability that the bride and groom choose the same tour (they choose independently)? - Probability 53061
One hundred people work in the office. Each of them spends an average of 25 minutes daily on the phone. A working day has 8 hours. What is the probability that ten workers will be on the phone simultaneously in one day? - Party
At the party, everyone clinked with everyone. Together, they clink $strng times. How many people were at the party?
- Combinations 6
Six purses Nine flaps 12 straps Every combination must include one purse, one flap, and one strap. How many are possible combinations? - Defect rate
A manufacturing machine has a 3% defect rate. If 9 items are chosen randomly, what is the probability that at least one will have a defect? - Probability 66424
There are 5 chocolate, 3 cottage cheese, and 2 apricot croissants in the bag. Croissants are randomly selected in bags. What is the probability of drawing 1 chocolate, 1 cheese, and 1 apricot croissant without returning? - How many 31
How many ways can a teacher select a group of 3 students to sit in the front row if the class has 13 students? - A pizza
A pizza place offers 14 different toppings. How many different three-topping pizzas can you order?
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