Question

В производственном отделе компании работают 26 человек, среди них 6 женщин. Наудачу выбрано 3 служащих. Найти вероятность того, что все они женщины

Answer 1

C6 по 3 * C 20 по 0 / C 26 по 3

Answer 2

Calculating the Probability of Selecting 3 Female Employees

To calculate the probability of randomly selecting 3 female employees out of 26 total employees in the production department, we can use the concept of combinations and probability.

The probability of selecting 3 female employees out of 6 can be calculated using the formula for combinations, which is given by:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

The number of favorable outcomes is the number of ways to choose 3 females out of 6, and the total number of possible outcomes is the number of ways to choose 3 employees out of 26.

Calculation

The number of ways to choose 3 females out of 6 can be calculated using the combination formula:

Number of ways to choose 3 females out of 6 = 6 choose 3 = 6! / (3!(6-3)!)

Substitute the values:

Number of ways to choose 3 females out of 6 = 6! / (3!(6-3)!) = (6 * 5 * 4) / (3 * 2 * 1) = 20

The total number of ways to choose 3 employees out of 26 can be calculated using the combination formula:

Total number of ways to choose 3 employees out of 26 = 26 choose 3 = 26! / (3!(26-3)!)

Substitute the values:

Total number of ways to choose 3 employees out of 26 = 26! / (3!(26-3)!) = (26 * 25 * 24) / (3 * 2 * 1) = 2600

Now, we can calculate the probability:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes) = 20 / 2600 ≈ 0.0077

Answer

The probability of randomly selecting 3 female employees out of 26 total employees in the production department is approximately 0.0077.