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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})



作者声明:本文包含人工智能生成内容。

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