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
- Fruits
We want to plant five fruit trees in the garden, of which three are apple trees and two pears. How many different ways can we organize them? - STRESSED word
Each letter in STRESSED is printed on identical cards, one letter per card, and assembled in random order. Calculate the probability that the cards spell DESSERTS when assembled. - Digits
How many odd four-digit numbers can we create from digits: 0, 3, 5, 6, and 7? (a) the figures may be repeated (b) the digits may not be repeated - Two groups
The group of 10 girls should be divided into two groups with at least four girls in each group. How many ways can this be done?
- Beads
How many ways can we thread four red, five blue, and six yellow beads onto a thread? - 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. - 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? - Chocolates
In the market, we have 3 kinds of chocolates. How many ways can we buy 8 chocolates? - Wagons
We have six wagons: two white, two blue, and two red. We assemble trains from them; wagons of the same color are exactly the same, so if we change only two white wagons on a train, it's still the same train because I don't know any difference. How many di
- Chocolates 38751
Jane wants to buy six chocolates in the store. The store offers only three species of chocolates. How many options does she have? - Kenneth 2
Kenneth has 100 pennies, 20 nickels, 10 dimes, and 4 quarters. How many ways can he choose coins that total 25 cents? - Divide
How many different ways can three people divide seven pears and five apples? - Six attractions
How many opportunities do you have if you want to complete ten rides on the fair, but there are only six attractions? - 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?
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