1. ## Combination problem

Ok, so I'm doing a project and I've run into a problem.

I have 5 rows of items.

3 items in the first row (1.1, 1.2, 1.3)
4 items in the second row (2.1, 2.2, 2.3)
5 items in the third row (3.1, 3.2, etc.)
4 items in the fourth row and
5 items in the fifth row

If I was allowed to pick one item from each row, how many possible combinations of items would there be? (eta: Yeah, I know I could count, but I bet there's an easier way to do it)

More importantly, what is this kind of problem called? I'm planning to do a bit more with this and I've love to know if there's an easy way to figure out what each of those combinations would be.

2. Originally Posted by quixotecoyote
Ok, so I'm doing a project and I've run into a problem.

I have 5 rows of items.

3 items in the first row (1.1, 1.2, 1.3)
4 items in the second row (2.1, 2.2, 2.3)
5 items in the third row (3.1, 3.2, etc.)
4 items in the fourth row and
5 items in the fifth row

If I was allowed to pick one item from each row, how many possible combinations of items would there be? (eta: Yeah, I know I could count, but I bet there's an easier way to do it)

More importantly, what is this kind of problem called? I'm planning to do a bit more with this and I've love to know if there's an easy way to figure out what each of those combinations would be.
You simply multiply the number of items in each row times each other. This is an application of combinations. Take $\displaystyle _{n}C_{r}$ for each individual row, where n is the number of items and r is the number you are choosing. r=1 for all of these so the combinations just the number of elements in the row. If you want the ways of independent situations to both occur, you multiply them.

3. Ah. Thank you. Somehow I didn't think it would be that easy.