To solve the problem of finding the number of straight lines formed by 10 points (4 of which are collinear), follow these steps:
Step 1: Total lines if all points are non-collinear
Any 2 distinct points form a line. For (n=10) points:
[ \binom{10}{2} = \frac{10 \times 9}{2} = 45 ]
Step 2: Adjust for collinear points
The 4 collinear points would normally form (\binom{4}{2}) lines, but they actually form only 1 line.
Compute the extra lines counted initially:
[ \binom{4}{2} = \frac{4 \times 3}{2} = 6 ]
The excess lines are (6 - 1 = 5) (since these 6 lines are replaced by 1).
Step 3: Calculate the final number of lines
Subtract the excess lines from the total:
[ 45 - 5 = 40 ]
Answer: (\boxed{40})
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