Question

List all the ways you can select two different members from S. The order in which you select the members

is not important. For example, AB is the same selection as BA.

S = {G, H, J, K, L}

Answer 1

{GH, GJ, GK, GL, HJ, HK, HL, JK, JL, KL}

Explanation:

We are asked to write down a list of all the possible ways we can select two different members from a group that is given to us. The order doesn't matter so we're talking about combinations.

First we are going to take the first term G and fix it so we can choose the second one, we get:

GH, GJ, GK, GL

Now, we take the second term H and fix it, we will not be able to choose the G here since HG is the same as GH and we already have that one in the previous list. In other words, we are going to be able to choose for the second term only the letters that are at the right of the H. So we get:

HJ, HK, HL

With a similar reasoning we take now the J and we get:

JK, JL

Finally, we take the K and we get:

KL.

Since we chose these different members using a specific order and logic, these are all the ones we get: {GH, GJ, GK, GL, HJ, HK, HL, JK, JL, KL}