Question

A elementary school art class teacher plans to display artwork next to the door of each of the classrooms in the school. Each classroom door will only have one piece of artwork displayed, and the school has 27 such doors. If the teacher has 11 sculptures, 10 sketches, and 12 oil paintings, what is the probability that 8 sculptures, 9 sketches, and 10 oil paintings are chosen to be displayed? Round your answer to 3 decimal places.

Answer 1

The probability that 8 sculptures, 9 sketches, and 10 oil paintings are chosen to be displayed is 0.2.

Step-by-step explanation:

This question is asking for the probability that 8 sculptures, 9 sketches, and 10 oil paintings are chosen to be displayed out of a total of 27 doors. To find the probability, we need to calculate the ratio of the number of ways we can choose the desired artworks to the total number of possible outcomes.

The total number of ways to choose 8 sculptures, 9 sketches, and 10 oil paintings from their respective groups is given by:

C(11, 8) * C(10, 9) * C(12, 10) = 165 * 10 * 66 = 108,900

The total number of possible outcomes, which is the total number of ways to choose any 8 artworks from the 11 sculptures, any 9 artworks from the 10 sketches, and any 10 artworks from the 12 oil paintings, is given by:

C(11, 8) * C(10, 9) * C(12, 10) = 165 * 45 * 66 = 544,500

Therefore, the probability that 8 sculptures, 9 sketches, and 10 oil paintings are chosen is:

108,900 / 544,500 = 0.2 (rounded to 3 decimal places)