Permutation Combination Question 2
Question 2 - 2024 (01 Feb Shift 2)
The lines $\mathrm{L}{1}, \mathrm{~L}{2}, \ldots, \mathrm{I}{20}$ are distinct. For $\mathrm{n}=1,2,3, \ldots, 10$ all the lines $\mathrm{L}{2 \mathrm{n}-1}$ are parallel to each other and all the lines $L_{2 n}$ pass through a given point $\mathrm{P}$. The maximum number of points of intersection of pairs of lines from the set $\left{\mathrm{L}{1}, \mathrm{~L}{2}, \ldots, \mathrm{L}_{20}\right}$ is equal to :
Show Answer
Answer (101)
Solution
$\mathrm{L}{1}, \mathrm{~L}{3}, \mathrm{~L}{5},–\mathrm{L}{19}$ are Parallel
$\mathrm{L}{2}, \mathrm{~L}{4}, \mathrm{~L}{6},–\mathrm{L}{20}$ are Concurrent
Total points of intersection $={ }^{20} \mathrm{C}{2}-{ }^{10} \mathrm{C}{2}-{ }^{10} \mathrm{C}_{2}+1$
$=101$
