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In how many ways can 2 students be selected from a group of 5 students in a debating competition?
25 ways
10 ways
15 ways
20 ways
Explanation
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In this case, you want to select 2 students from a group of 5 students.
You can choose the first student in
5
5 ways.
Once the first student is chosen, there are
4
4 remaining students to choose from for the second student.
So, the total number of ways to select 2 students from 5 is
5
You're welcome
×
4
=
20
5×4=20.
However, since the order of selection doesn't matter (selecting students A and B is the same as selecting B and A), we need to divide by
2
2 to avoid counting each pair twice.
Therefore, the number of combinations of 2 students from 5 is
20
÷
2
=
10
20÷2=10.
This method is a simpler way to arrive at the answer without directly using the combination formula.