Permutation Combination and Probability - Sampling with / without ordering

The next parameter on which sampling can be classified is Sampling based on whether Ordering (Arrangement) of the elements selected is considered or not.

In this case too, as in the case of sampling with or without replacement let us look at two examples that will help us learn the concept better.

Example 1. In how many ways can a group of students elect a President and a Vice President from 10 contestants if a person cannot hold more than one post?

It is quite obvious that the president can be elected from the 10 contestants in 10 ways and the vice president can be elected from the remaining 9 students in 9 ways. As the group of students elect a president and a vice president, the total number of ways = 10 * 9 = 90.

Let the contestants be recognized by the letters A to J.
Any one of the A to J could have been elected as the president.
Now, let us say, B was elected the president. Then, anyone of the remaining 9 contestants can be elected as vice president. Say, D was elected vice president.

You will realize that the 90 outcomes include the case of "B" being the president and "D" being the vice president and "B" being the vice president and "D" being the president.

i.e., for B and D being the two contestants who were elected, there are two possibilities - BD or DB and therefore, this is an example of sampling with Ordering