Question and Answers Forum

All Questions      Topic List

Permutation and Combination Questions

Previous in All Question      Next in All Question      

Previous in Permutation and Combination      Next in Permutation and Combination      

Question Number 112812 by Aina Samuel Temidayo last updated on 09/Sep/20

There are 2016 straight lines drawn on  a board such that (1/2) of the lines are  parallel to one another. (3/8) of them  meet at a point and each of the  remaining ones intersect with all  other lines on the board. Determine  the total number of intersections  possible.

$$\mathrm{There}\:\mathrm{are}\:\mathrm{2016}\:\mathrm{straight}\:\mathrm{lines}\:\mathrm{drawn}\:\mathrm{on} \\ $$$$\mathrm{a}\:\mathrm{board}\:\mathrm{such}\:\mathrm{that}\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{of}\:\mathrm{the}\:\mathrm{lines}\:\mathrm{are} \\ $$$$\mathrm{parallel}\:\mathrm{to}\:\mathrm{one}\:\mathrm{another}.\:\frac{\mathrm{3}}{\mathrm{8}}\:\mathrm{of}\:\mathrm{them} \\ $$$$\mathrm{meet}\:\mathrm{at}\:\mathrm{a}\:\mathrm{point}\:\mathrm{and}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{remaining}\:\mathrm{ones}\:\mathrm{intersect}\:\mathrm{with}\:\mathrm{all} \\ $$$$\mathrm{other}\:\mathrm{lines}\:\mathrm{on}\:\mathrm{the}\:\mathrm{board}.\:\mathrm{Determine} \\ $$$$\mathrm{the}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{intersections} \\ $$$$\mathrm{possible}. \\ $$

Commented by ahmediname last updated on 10/Sep/20

-241.31

Commented by Aina Samuel Temidayo last updated on 10/Sep/20

What do you mean?

$$\mathrm{What}\:\mathrm{do}\:\mathrm{you}\:\mathrm{mean}? \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com