Elements of combinatorics. Combinatorics

Required select ordered three-element subsets of a set containing 40 elements, i.e. find the number of placements without repetitions from 40 elements of 3.

A = \u003d 38 * 39 * 40 \u003d 59280
40!
37!
40
3

check yourself

1. Choose four out of seven different books . In how many ways can this be done?

SOLUTION

check yourself

• Four are selected from seven different books . In how many ways can this be done?

Solution.

A \u003d \u003d 840
4
7
7!
3!

check yourself

Ten teams participate in the football championship . How many different possibilities are there for teams to take the first three places?

SOLUTION

check yourself

Ten teams participate in the football championship . How many different possibilities are there for teams to take the first three places?

Solution.

A \u003d \u003d 720
7!
3
10
10!

check yourself

3. 7 subjects are studied in the class . On Wednesday there are 4 lessons , and all are different. In how many ways can you schedule Wednesday?

SOLUTION

check yourself

• 7 subjects in the class . On Wednesday there are 4 lessons , and all are different. In how many ways can you schedule Wednesday?

Solution.

A \u003d \u003d 840
4
7
7!
3!

Placements with repetitions

• Placements with repetitions - compounds containing n elements selected from elements of m different types ( ) and differing from one another either in the composition or the order of the elements.
• Their number , assuming an unlimited number elements of each type is