First slide

Combinations

Question

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

Moderate

A

32
B

64
C

76
D

104

Solution

The required number of points
$\begin{array}{l} =^{8} C_{2} \times 1 +^{4} C_{2} \times 2 + (^{8} C_{1} \times^{4} C_{1}) \times 2 \\ = 28 + 12 + 32 \times 2 = 104 \end{array}$

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