Combinations with repetition
The calculator finds the number of combinations of the k-th class from n elements with 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 more than once (repeated).Calculation:
Ck′(n)=(kn+k−1) n=10 k=4 C4′(10)=C4(10+4−1)=C4(13)=(413)=4!(13−4)!13!=4⋅3⋅2⋅113⋅12⋅11⋅10=715
The number of combinations with repetition: 715
A bit of theory - the foundation of combinatorics
Combinations with repeat
Here we select k element groups from n elements, regardless of the order, and the elements can be repeated. k is logically greater than n (otherwise, we would get ordinary combinations). Their count is:Ck′(n)=(kn+k−1)=k!(n−1)!(n+k−1)!
Explanation of the formula - the number of combinations with repetition is equal to the number of locations of n − 1 separators on n-1 + k places. A typical example is: we go to the store to buy 6 chocolates. They offer only 3 species. How many options do we have? k = 6, n = 3.
Foundation of combinatorics in word problems
- 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? - Sons
The father has six sons and ten identical, indistinguishable balls. How many ways can he give the balls to his sons if everyone gets at least one? - 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? - Cinema
How many ways can 11 free tickets to the premiere of "Jáchyme throw it in the machine" be divided between 6 pensioners?
- Boys and girls
There are 11 boys and 18 girls in the classroom. Three pupils will answer. What is the probability that two boys will be among them? - Cards
How many ways can you give away 32 playing cards to 7 player? - Honored students
Of the 25 students in the class, ten are honored. How many ways can we choose five students from them if there are to be exactly two honors between them? - Bouquets
In the flower shop, they sell roses, tulips, and daffodils. How many different bouquets of 5 flowers can we make? - Word MATEMATIKA
How many words can be created from the phrase MATEMATIKA by changing the letters' order, regardless of whether the words are meaningful?
- Three workplaces
How many ways can we divide nine workers into three workplaces if they need four workers in the first workplace, 3 in the second workplace, and 2 in the third? - Salami
We have six kinds of salami that have ten pieces and one kind of salami that has four pieces. How many ways can we distinctly choose five pieces of salami? - Combinations 6
Six purses Nine flaps 12 straps Every combination must include one purse, one flap, and one strap. How many are possible combinations? - The gems
The jeweler selects four gems for the ring. It has rubies, emeralds, and sapphires. How many options does he have? - Families 2
Seven hundred twenty-nine families have six children each. The probability of a girl is 1/3, and the likelihood of a boy is 2/3. Find the number of families having two girls and four boys.
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