I got this prism
How many lines can be formed by the vertices of the prism and the points I and J?
- Combinations between the vertices = $^8C_2 = 28$
- Combinations of 1 vertex and either I or J = $^8C_1 \cdot ^2C_1 = 16$
Combinations between I and J = $1$
Total = $28 + 16 + 1 = 45$
But my book says the solution is 41. What did I do wrong?
I admit the problem isn't very clear. I am not sure if what is wanted is only the combinations between one vertex and either I or J or the combinations between all of them. I copied the problem as it is.