Question

You are choosing numbers from the set S ={A, B, C, D, E, F, G, H}. Let x = the number of ways to choose 3 letters from S without replacement (order doesn’t matter). Which option below is equivalent to x?

Answer 1

The number of ways to choose 5 letters from S without replacement

Answer 2

Given set S = {A, B, C, D, E, F, G, H}
There are 8 elements in set S and we are to choose 3 letters at random, the number of ways to choose such is x. It is simply similar to choosing 5 letters at random, which is also equal to x. Since order doesn't matter, n! / (n-m)! where n = 8 and m = 3, which is 336 ways.