Question

There are 8 students in the chess club. The club moderator selects 3 of them to go to a chess tournament. How many different groups of 3 students can be selected?

1) 28
2) 56
3) 84
4) 120

Answer 1

There are 56 different groups of 3 students that can be selected from the 8 students in the chess club, using the formula for combinations.

Step-by-step explanation:

The question posed is related to combinatorics, a topic within mathematics that deals with counting combinations and permutations. Specifically, the question asks how many different groups of 3 students can be selected from 8 students in the chess club. To answer this, we use the combination formula which is C(n, k) = n! / (k!(n - k)!), where 'n' is the total number of items to choose from, 'k' is the number of items to choose, and '!' denotes factorial.

In this case, we have 8 students and we want to select groups of 3, so our formula is C(8, 3) = 8! / (3!5!) = (8 \times 7 \times 6) / (3 \times 2 \times 1) = 56. Therefore, there are 56 different groups of 3 students that can be selected. The correct answer from the options provided is 2) 56.