Each section in the first year of plus two course has...

Each section in the first year of plus two course has exactly 40 students. If there are 5 sections, in how many ways can a set of 4 student representatives be selected, one from each section?
(a) 2560000
(b) 246500
(c) 2240000
(d) 2360000

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Combination Selection

Combination selection involves choosing a subset of items from a larger set when the order of selection does not matter. In problems where a representative must be chosen from several groups, it is often necessary to decide which groups will be included in the selection process, with the number of ways of making this choice calculated using the binomial coefficient.

Fundamental Principle of Counting

This principle states that if one event can occur in m ways and a second independent event can occur in n ways, then the two events together can occur in m × n ways. It is used to systematically count the total number of outcomes where several independent choices are made, which is central to solving problems that involve selecting individuals or items from different groups.

Selection from Disjoint Groups

When representatives are to be selected from separate and non-overlapping groups, each group functions independently. This key concept involves making selections within each group while ensuring that the overall choices satisfy the problem’s constraints. The outcomes from each independent group are then combined using the multiplication principle to yield the total number of ways the selection can be made.

Transcript

Please give Ace some feedback