If from a set containing n elements, m elements are selected in turn , and the selected element is returned each time, then the number of ways to make an unordered sample is the number of combinations with repetitions - is
Historical reference
The greatest Indian mathematician Bhaskara Akaria (1114–1185) also studied various types of combinatorial compounds. He owns the treatise "Sidhanta-Shiromani" ("The Crown of Teaching"), rewritten in the 13th century. on strips of palm leaves. In it, the author gave verbal rules for finding and, indicating their applications and placing numerous examples
Usage example
Task #1
How many sets of 7 cakes can you make if you have 4 types of cakes?
Solution:
Usage example
Task #2
How many bones are there in a typical domino game?
Solution : Domino bones can be considered as combinations with repetitions of two of the seven digits of the set (0,1,2,3,4,5,6). The number of all such combinations is
check yourself
Task 1.
In the cafeteria of the Gymnasium, 5 varieties of pies are sold : with apples, with cabbage, potatoes, meat and mushrooms. In how many ways can you make a purchase out of 10 cakes?
SOLUTION
TASK #1
Solution:
Answer: 1001
check yourself
Task 2.
The box contains balls of three colors - red, blue and green. In how many ways can you make a set of two balls?
SOLUTION
TASK #2
Solution:
Answer: 6
check yourself
Task 3.
In how many ways can 4 coins be chosen from 4 5-kopeck coins and from 4 2-kopeck coins?
