SOLUTION: The number of straight lines that can be formed by joining 10 points no three of which are in the same straight line except 7 of them which are in the same straight line, is

Suppose the 7 points points A through G are in the same straight line.

That's 1 straight line.

Suppose H, I, J, are not, and that no three other than A through G are 
in a straight line.

We can connect the 3 points that aren't in a straight line three
ways, HI, HJ, and IJ.

That's 3 more straight lines.

We can connect H and each of the 7 points A through G

That's 7 more straight lines

We can connect I and each of the 7 points A through G

That's 7 more straight lines 

We can connect J and each of the 7 points A through G

That's 7 more straight lines.

Total 1+3+7+7+7 = 25 lines

Edwin