Question

The number of combinations for selecting 6 elements from 13 distinct elements is

Answer 1

Order is allowed" means different permutations of the same objects are considered different.

For example, number of ways of picking 2 objects out of {a,b,c}{a,b,c}with "order allowed" will include {ab,ba,bc,cb,ac,ca}{ab,ba,bc,cb,ac,ca}. A good way of understanding "order allowed but repetition not allowed" in your problem is to think you are picking the six objects one at a time from the ten objects. For instance, in my example ababrepresents picking aa in the first pick and picking bb in the second.

The way to count with "order allowed but repetition not allowed" is to see how many choices you have at each pick and multiply them. For my example, I had three choices for the first pick viz. a,b,ca,b,c and for my second pick, i have two choices left. So the total number of ways is 3×2=63×2=6 which is the total number of possibilities in our enumeration viz. {ab,ba,bc,cb,ac,ca}{ab,ba,bc,cb,ac,ca}