A shipment of 50 parts contains 11 defective parts. Suppose 3 parts are selected at random, without replacement, from the shipment. What is the probability that exactly 2 parts are not defective?

anyone? thanks!

23.44 To find the probability that exactly 2 parts are not defective, we need to calculate the number of favorable outcomes (selecting 2 non-defective parts) divided by the total number of possible outcomes (selecting any 3 parts).

1. Calculate the number of favorable outcomes:
Since there are 11 defective parts in a shipment of 50, the number of non-defective parts is 50 - 11 = 39.
To select exactly 2 non-defective parts, we have to consider all possible combinations of selecting 2 parts out of the 39 non-defective parts.
This can be calculated using the combination formula: nCr = n! / (r! * (n - r)!), where n is the total number of parts and r is the number of non-defective parts to be selected.

So, the number of favorable outcomes = 39C2 = 39! / (2! * (39 - 2)!)

2. Calculate the total number of possible outcomes:
To select any 3 parts from the shipment, we need to consider all possible combinations of selecting 3 parts out of the total 50 parts.
This can be calculated using the combination formula: nCr = n! / (r! * (n - r)!), where n is the total number of parts and r is the number of parts to be selected.

So, the total number of possible outcomes = 50C3 = 50! / (3! * (50 - 3)!)

3. Calculate the probability:
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes

So, the probability of exactly 2 parts not being defective = number of favorable outcomes / total number of possible outcomes.