3. In a store where there are 4 types of balls , they decided to put 8 balls in a row . In how many ways can this be done if their location matters?
Solution.
4 different types of balls, 8 positions, i.e. the number of different placements will be = 65536.
Answer : 65536 ways.
Check yourself!
six buttons of one of the four colors be sewn on a clown costume in a line to get a pattern?
SOLUTION
Check yourself!
six buttons of one of the four colors be sewn on a clown costume in a line to get a pattern?
Solution.
Apparently, the number of buttons of each type is large, so to determine the number of ways, you can use the placement formula with repetitions.
It is equal to = 1296 (6 positions and 4 types).
Answer: 1296 ways.
Combinations
Combinations - compounds containing m items out of n , differing from each other in at least one item .
Combinations are finite sets in which the order does not matter.
Combinations
The formula for finding the number of combinations without repetitions:
Historical reference In 1666, Leibniz published Discourses on Combinatorial Art. In his work, Leibniz, introducing special symbols, terms for subsets and operations on them, finds all k -combinations of n elements, deduces the properties of combinations: , , Usage example: In how many ways can two attendants be chosen from a class of 25 students? m = 2 ( required number of attendants ) n = 25 (total students in the class) Solution: Check yourself! 1) In how many ways can three students be delegated to an interuniversity conference of 9 members of a scientific society? SOLUTION
Check yourself!