Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • On the sides AB,BC,CA, of  3,4,5 distibct points (excuding vertices A,B,C) are respectively ch

On the sides AB,BC,CA, of \triangle ABC 3,4,5 distibct points (excuding vertices A,B,C) are respectively chosen. the number of trangles that can be constructed using these chosen points as vertices are:

Option: 1

210


Option: 2

205


Option: 3

215


Option: 4

220


Answers (1)

best_answer

Single triangle needs 3 vertices

Case 1:

One point in each side

=\;^3C_{1} \times \;^4C_{1} \times\;^{5}C_{1}=60

Case 2:

1 point from side AB & 2 points from BC

=\;^{3}C_{1} \times\;^{4}C_{2}=12

Case 3:

1 point from side BC & 2 points from AC

=\;^{4}C_{1} \times\;^{5}C_{2}=40

Case 4:

1 point from side AC & 2 points from BC

=\;^{5}C_{1} \times\;^{4}C_{2}=30

Case 5:

1 point from side AB & 2 points from AC

=\;^{3}C_{1} \times\;^{5}C_{2}=30

Case 6:

1 point from side AC & 2 points from AB

=\;^{5}C_{1} \times\;^{3}C_{2}=15

Total Triangle = 60+18+12+40+30+30+15=205

 

Second Approach

Totel vertices =3+4+5=12

\;^{12}C_{23}-\;^3C_{3}-\;^4C_{3}-\;^5C_{3}=220-1-4-10=205

Posted by

sudhir kumar

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026 Paper 2 Toppers: 4 score 100 percentile; most from Kerala, one female topper
anam-khan

JEE Mains 2026 paper 2 result out on jeemain.nta.nic.in
anam-khan

JEE Mains 2026 session 2 B.Arch, B.Planning final answer key out, no question dropped

Latest Question