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?

Answer 1

Answer:This problem involves using the concept of probability. We can use the formula for probability:

Probability = (number of desired outcomes) / (total number of possible outcomes)

First, let's calculate the total number of possible outcomes. Since there are 27 doors and each door can only have one piece of artwork, there are a total of 27 possible outcomes.

Next, let's calculate the number of desired outcomes. The teacher wants to display 8 sculptures, 9 sketches, and 10 oil paintings. We can choose 8 sculptures from the 11 available in C(11,8) ways (using the combination formula), 9 sketches from the 10 available in C(10,9) ways, and 10 oil paintings from the 12 available in C(12,10) ways. To find the total number of desired outcomes, we can multiply these together:

number of desired outcomes = C(11,8) * C(10,9) * C(12,10)

= (165) * (10) * (66)

= 108,900

Finally, we can plug these values into the formula for probability:

Probability = (number of desired outcomes) / (total number of possible outcomes)

= 108,900 / 27

= 4,033.3 (rounded to one decimal place)

However, probabilities cannot be greater than 1. Therefore, the probability of displaying 8 sculptures, 9 sketches, and 10 oil paintings is 1.