Elements of combinatorics. Combinatorics

Usage example

5 schoolchildren came to the library, which has many identical textbooks in ten subjects , each of whom wants to take a textbook. The librarian writes in the journal in order the names (without number) of the borrowed textbooks without the names of the students who took them. How many different lists could appear in the magazine?

The solution of the problem

Since the textbooks for each subject are the same, and the librarian writes down only the name (without a number), the list is a repeating layout . the number of elements of the original set is 10, and the number of positions is 5.

Then the number of different lists is

= 100000.

Answer : 100000

Check yourself!

1. Phone number consists of 7 digits. What is the maximum number of calls the loser Petya can make before he guesses the correct number.

SOLUTION
SOLUTION
SOLUTION

Check yourself!

1. Phone number consists of 7 digits. What is the maximum number of calls the loser Petya can make before he guesses the correct number.

Solution.

Because numbers can be repeated, then everything is possible

different numbers.

If Petya is unlucky, he must will call 10 million times.

Answer : 10000000 .

Check yourself!

2. In how many ways can you write a word made up of four letters of the English alphabet?

SOLUTION
SOLUTION

Check yourself!

2. In how many ways can you write a word made up of four letters of the English alphabet?

Solution.

There are 26 letters in the English alphabet, letters can be repeated, which means that the number of words is

(26 elements and 4 positions)

Answer:

Check yourself!

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