Permutation Combination Question 2
Question 2 - 2024 (01 Feb Shift 2)
The lines $L _1, L _2, \ldots, I _{20}$ are distinct. For $n=1,2,3, \ldots, 10$ all the lines $L _{2 n-1}$ are parallel to each other and all the lines $L _{2 n}$ pass through a given point $P$. The maximum number of points of intersection of pairs of lines from the set ${L _1, L _2, \ldots, L _{20} }$ is equal to :
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Answer (101)
Solution
$L _1, L _3, L _5,–L _{19}$ are Parallel
$L _2, L _4, L _6,–L _{20}$ are Concurrent
Total points of intersection $={ }^{20} C _2-{ }^{10} C _2-{ }^{10} C _2+1$
$=101$
