I have a bag with 6 marbles numbered from 1 to 6. Mathew has a bag with 12 marbles numbered from 1 to 12. Matthew chooses one marble from his bag and I choose two from mine. In how many ways can we choose the marbles (where the order of my choices does matter) such that the sum of the numbers on my marbles equals the number on his?
Any two numbers that you choose can match a number from his.
There are 15 different sums that you can get: 1/2 1/3 1/4 1/5 1/6 2/3 2/4 2/5 2/6 3/4 3/5 3/6 4/5 4/6 5/6
Each of these sums can be chosen in two ways, so there are a possible 30 different selections for you.
If Mathew chooses first, then any number that he chooses (provided that his choice is larger than 2 and smaller than 12
can be matched by the choices listed above.