Answer:
a= 2 trains of length
b=
For a train with the length of 6, you can make 4 trains of length.
For a train with the length of 7, you can make 7 trains of length.
For a train with the length of 8, you can make 12 trains of length.
c= The relation of the length and the number of trains you are able to make is determined by the number of permutations (unsure whether this is the right term??) or number of ways you can add numbers together to get the length. For example, a train with the length of 6 would have 4 trains of length because 4+2, 2+4, 2+2+2, and 3+3 all add up to 6.
Explanation:
To find the answer for a, simply know that the two permutations are 2+3 and 3+2, so there are 2 ways to add up to 5.
To find all of the answers for b, you have to figure out the number of ways to add up to 6 (the order matters!). For a train with the length of 6, there are 4 ways: 4+2, 2+4, 2+2+2, and 3+3. For a train with the length of 7, there are 7 ways: 2+2+3, 2+3+2, 3+2+2, 3+4, 4+3, 5+2, and 2+5. And lastly, for a train with the length of 8, there are 12 ways: 2+2+2+2, 3+3+2, 2+3+3, 3+2+3, 4+2+2, 2+4+2, 2+2+4, 2+6, 6+2, 5+3, 3+5, and 4+4.