Time for a quick geometry lesson.
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Answer: 36.
Polygon (Pantagon)
ABC, ACD, ADE, BCD, BDE,BEA, CDE, CEA,DAB, EBC = No. of triangles = n = 10
AB, BC, CD, DE, AE = No of sides = r = 5
Total Number of Triangles =?
We use combination method: 10c5 = 10!/5!(10-5)!=10!/5!5!=(10.9.8.7.6.5.4.3.2.1)/(5.4.3.2.1.5.4.3.2.1)=36
Note: nCr = n!/r!(n-r)!
Answer contributed by: Dr. Nadeem Hussain Qureshi (dnhq1970@gmail.com)
Actually their are 35 only….not 36….your method is wrong!
You are right!
35
C(10,5)=252
C(10,5)=252
Polygon (Pantagon)
ABC, ACD, ADE, BCD, BDE,BEA, CDE, CEA,DAB, EBC = No. of triangles = n = 10
AB, BC, CD, DE, AE = No of sides = r = 5
Total Number of Triangles =?
We use combination method: 10c5 = 10!/5!(10-5)!=10!/5!5!=(10.9.8.7.6.5.4.3.2.1)/(5.4.3.2.1.5.4.3.2.1)=36
Note: nCr = n!/r!(n-r)!
Dr. Nadeem Hussain Qureshi (dnhq1970@gmail.com)
Nicely solved 🙂
Thanks Nadeem
Posting it to the blog
The combination answer is wrong,it cannot be 36!
And total triangles could be 35 and not 36.