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.