Question

There are five students who are interested in presenting their final project to the class, but there is only time for three presentations. The five students are Amy, Bob, Chun, Dan and Ed.

How many possible groupings of three out of the five are possible?

Answer 1

The number of possible groupings for selecting three out of five students is 10, calculated using the combination formula C(n, k) = n! / (k! * (n-k)!).

Step-by-step explanation:

The question asks for the number of possible groupings when selecting three students out of five for presentations. To solve this, we use the concept of combinations in mathematics. In a combination, the order of selection does not matter. The number of combinations can be calculated using the formula for combinations, 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.

So, for our case with five students (n = 5) and choosing three of them (k = 3), the calculation is:

C(5, 3) = 5! / (3! * (5-3)!) = (5 × 4 × 3!)/(3! × 2!) = (5 × 4)/2 = 10.

There are 10 possible groupings of three students out of the five.