Question

В партии из 12 деталей имеется 9 стандартных . Найти вероятность того , что среди семи взятых наугад деталей шесть стандартных

Answer 1

Вероятность P=C₉⁶*C₃¹/C₁₂⁷=[9!*3/(6!*3!)]/[12!/(7!*5!)]=7/22. Ответ: 7/22.

Answer 2

Problem Analysis

We are given a set of 12 parts, out of which 9 are standard. We need to find the probability of selecting 6 standard parts out of 7 randomly chosen parts.

Solution

To find the probability, we can use the concept of combinations. The number of ways to choose 6 standard parts out of 9 is given by the combination formula:

C(n, k) = n! / (k!(n-k)!)

Where: - n is the total number of parts (9 in this case) - k is the number of standard parts (6 in this case)

Let's calculate the probability using this formula.

Calculation

Using the combination formula, we can calculate the number of ways to choose 6 standard parts out of 9:

C(9, 6) = 9! / (6!(9-6)!) = 9! / (6!3!) = (9 * 8 * 7) / (3 * 2 * 1) = 84

Now, we need to calculate the total number of ways to