Question

Hey workers are cleaning a large house: five are needed to clean windows, two to clean the carpets, and one to clean the rest of the house. How many different ways can these tasks be assigned to your workers?

A) 40 ways
B) 60 ways
C) 90 ways
D) 120 ways

Answer 1

There are 168 different ways to assign the tasks to the eight workers, which is calculated using combinations for worker assignment.

Step-by-step explanation:

The student asked about the number of different ways tasks can be assigned to eight workers, given that five are needed to clean windows, two to clean carpets, and one to do the rest of the house. To determine this, we use combinations to assign the different tasks.

Firstly, we select five workers for the windows from the eight available, which can be done in 8 choose 5 ways (denoted as 8C5). Once those five workers are chosen, we are left with three workers. We then select two of those to clean the carpets, which can be done in 3 choose 2 ways (denoted as 3C2). The remaining one worker will clean the rest of the house.

The total number of different ways to assign these tasks is therefore the product of these two combinations:

8C5 × 3C2 = (8! / (5!3!)) × (3! / (2!1!)) = (56) × (3) = 168 ways

So, there are 168 different ways to assign the tasks.