First slide

Combinations

Question

The maximum possible number of points of intersection of 7 straight lines and 5 circles is:

Moderate

A

111
B

109
C

107
D

105

Solution

Maximum possible number of points of intersection of 7 lines is $^{7} C_{2} = 21$
Maximum possible number of points of intersection of 5 circles in $2 (^{5} C_{2}) = 20$
$[∵$ two circles can intersect in two distinct points.]
Maximum possible number of points of intersection of 5 circles and 7 lines is 2(5) (7) = 70
Thus, maximum possible number of points of intersection is 21 + 20 + 70 = 111.

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