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
- Contestants 67104
The contestants have to create an ice cream sundae containing three different types of ice cream. They can use cocoa, yogurt, vanilla, hazelnut, punch, lemon and blueberry ice cream. How many different ice cream sundaes can the contestants create? - Kenneth 2
Kenneth has 100 pennies, 20 nickels, 10 dimes, and 4 quarters. How many ways can he choose coins that total 25 cents? - Five-digit numbers
How many different five-digit numbers can be created from the number 2,3,5 if the number 2 appears in the number twice and the number 5 also twice? - Six attractions
How many opportunities do you have if you want to complete ten rides on the fair, but there are only six attractions? - The gems
The jeweler selects four gems for the ring. It has rubies, emeralds, and sapphires. How many options does he have? - Twelve flowers
A florist has roses, tulips, daffodils, and carnations to use in flower arrangements. If she were to make an arrangement using 12 flowers, how many different combinations of these four types of flowers would be possible? - Points in space
There are n points, of which no three lie on one line and no four lies on one plane. How many planes can be guided by these points? How many planes are there if there are five times more than the given points? - 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? - 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? - 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? - Cinema
How many ways can 11 free tickets to the premiere of "Jáchyme throw it in the machine" be divided between 6 pensioners? - Combinations 6
Six purses Nine flaps 12 straps Every combination must include one purse, one flap, and one strap. How many are possible combinations? - Three reds
What is the probability that all three of the seven cards will be red if three cards are drawn? - 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? - Cards
From a set of 32 cards, we randomly pull out three cards. What is the probability that it will be seven kings and an ace?
more math problems »