A student must answer 3 out of 5 essay questions on a test. In how many different ways can the student select the question?
1 Answer
Explanation:
We can solve this using the number of combinations of
When solving these types of problems, you need to determine whether you are looking for combinations or permutations.
A permutation is concerned with the elements in a set as well as the order in which they appear.
Example:
The number of permutations of
These would be:
ABC
ACB
BAC
BCA
CAB
CBA
Notice that all contain the same elements, but they are arranged in a different order.
For the number of combinations of ABC taken 3 at a time, there is only 1. This is:
ABC
This is because combinations are only concerned with the elements themselves not in the order they are arranged
For our problem we need combinations, because we are not interested in the order the questions are in, only that they are different questions.
Combinations are represented by:
Where
To make this clearer:
We have 5 things, so
Putting these in:
So there are