Question

Elena is managing a construction project. She has 7 workers available to work on a given day, and she needs to

select 5 of them.
How many different sets of 5 workers can Elena choose?

Answer 1

Elena can choose from 21 different sets of 5 workers from a group of 7 available workers for her construction project. The calculation is based on the combination formula which considers the total number of items and the number of items to be chosen, with the order of selection being irrelevant.

Step-by-step explanation:

Elena needs to choose 5 workers from a group of 7 available workers for a construction project. This situation is an example of a combination, where the order of selection does not matter. To calculate the number of different sets of 5 workers Elena can choose, we use the combination formula, which is nCr = n! / (r!(n-r)!), where n is the total number of items, r is the number of items to choose, and ! denotes factorial.

In this case, n = 7 and r = 5. Plugging these values into the formula gives us:

7C5 = 7! / (5!(7-5)!) = (7x6) / (2x1) = 42 / 2 = 21

Therefore, Elena can choose from 21 different sets of 5 workers for her construction project.