Question

The greatest possible number of points of intersection of 8 straight lines and 4 circles is________.

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Answer 1

Case 1: Two lines can intersect maximum at one point.

Maximum number of intersection = ${}^8{C}_2\times 1$

Case 2: Two circles can intersect maximum at two points.

Maximum number of intersection = ${}^4{C}_2\times 2$

Case 3: circle and line can intersect maximum at two points.

Maximum number of intersection = = ${(}^8{C}_1{\times }^4{C}_1)\times 2$
The required number of points ${=}^8{C}_2\times 1{+}^4{C}_2\times 2+{(}^8{C}_1{\times }^4{C}_1)\times 2$
$=28+12+32\times 2=104$