Actually, the correct mathematical answer is 1,440, but you are on the right track by calculating the different differences first.
We see that:
The 1st #, three, has 4 different differences (choices).
The 2nd #, five, has 3 different differences (choices).
The 3rd #, two, has 4 different differences (choices).
The 4th #, ten, has 2 different differences (choices).
The 5th #, fifteen, has 3 different differences (choices).
However, we do not add together these differences to get 18.
Instead, we multiply: 4 x 3 x 4 x 2 x 3 = 288 total choices.
My explanation for this is there is no order as to which pair we subtract first. For example, we can begin with 3 - 5 or we can begin with 3 - 10. In this sense, order does not matter.
Lastly, we multiply: 288 x 5 = 1,440 total ways b/c again order does not matter. There are 5 different "sets" of combinations altogether. For example, we can begin with 5 - 3 followed by 10 - 2.
We see that:
The 1st #, three, has 4 different differences (choices).
The 2nd #, five, has 3 different differences (choices).
The 3rd #, two, has 4 different differences (choices).
The 4th #, ten, has 2 different differences (choices).
The 5th #, fifteen, has 3 different differences (choices).
However, we do not add together these differences to get 18.
Instead, we multiply: 4 x 3 x 4 x 2 x 3 = 288 total choices.
My explanation for this is there is no order as to which pair we subtract first. For example, we can begin with 3 - 5 or we can begin with 3 - 10. In this sense, order does not matter.
Lastly, we multiply: 288 x 5 = 1,440 total ways b/c again order does not matter. There are 5 different "sets" of combinations altogether. For example, we can begin with 5 - 3 followed by 10 - 2.
