Answer:
When we have a set of N elements, the number of combinations of K elements (such that N ≤ K) from these N elements is:
Then if we have 8 different types of carpet, and we want to see how many different samples of 3 types we can choose, we just need to replace N by 8, and K by 3 in the above equation:
So there are 56 different samples.
Now we can do the same, but this time we want to use 5 types of carpet, then we will have K = 5.
Again, we have 56 different samples.