Elements of combinatorics. Combinatorics

TASK #3

Solution: The order in which coins are chosen is not important, and examples of joins are {5,5,5,5}, {2,2,2,2}, {5,2,5,5}, etc. This is a problem about the number of combinations of two types of coins in four with repetitions .

Answer: 5

check yourself

Task 4.

How many dominoes will there be if all numbers are used in their formation?

SOLUTION

TASK #4

Solution: The number of dominoes can be considered as the number of combinations of 10 numbers of 2 with repetitions.

Answer: 55

check yourself

Task 5.

The palette of the young impressionist consists of 8 different colors. The artist takes any of the paints at random with a brush and puts a colored spot on the paper. Then he takes the next brush, dips it in any of the paints and makes a second spot in the neighborhood. How many different combinations are there for the six spots?

SOLUTION

TASK #5

Solution:

Answer: 1716

Probability theory

Basic concepts

Stages of development of the theory of probability

• 2nd half of the 16th century - the first tasks
• on the theory of probability.
• Late 17th - early 19th century
• formation as an independent
• scientific discipline.
• The end of the 19th - the end of the 20th century -
• modern stage of development.

L. Pacioli
D. Cardano
N. Tartaglia
B. Pascal
I. Bernoulli
A.Moivre
P.Laplace
S. Poisson
P.L. Chebysh ev
A.A.Markov
A.M. Lyapunov
A.Ya. Khinchin
A.N. Kolmogorov

Basic concepts

• Stochastic experiment
• (trial, experience) -
• This is an experiment, the results of which cannot be predicted in advance.
• Examples.
• 1. Tossing a coin;
• 2. Shot at the target;
• 3. Throwing a dice (dice);
• 4. Measurement of a physical quantity (product length, humidity or temperature, pressure)