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The maximum number of points of intersection of five lines and four circles is

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a

60

b

72

c

62

d

none of these

answer is C.

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Detailed Solution

Two circles intersect at two distinct points. Two straight lines intersect at one point. One circle and one straight line intersect at two distinct points. Then the total numbers of points of intersections are as follows:

Number of ways of selection	Points of intersection
Two straight lines: $^{5} C_{2}$	$^{5} C_{2} \times 1 = 10$
Two circles: $^{4} C_{2}$	$^{4} C_{2} \times 2 = 12$
One line and one circle: $^{5} C_{1} \times^{4} C_{1}$	$^{5} C_{1} \times^{4} C_{1} \times 2 = 40$
Total	62

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