Determine whether the following involves a permutation or combination.
A medical researcher needs 55 people to test the effectiveness of an experimental drug. If 300 people have volunteered for the test, in how many ways can 55 people be selected?
Solution:-
A permutation is an ordered arrangement of a given group of items. A combination is a group of items taken without regard to their order.
Thus, the difference between the two is that permutation problems involve situations in which order matters, while combination problems involve situations in which the order of items makes no difference.
Look at the problem you are given. A group of 55, out of the 300 people who volunteered, are to be selected for a medical research test.
The order in which the 55 people are selected dose not matter because they are not being picked to perform different roles. The volunteers are all being selected to test the same drug.
Since order dose not matter, this problem involves a combination.