No. of triangles

Probability Level 3

The number of triangles that can be formed with 10 points as vertices , n of them being collinear , is 110. Then n is

5 3 6 4

Akhil Bansal by Akhil Bansal , 22, India

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1 solution

Akhil Bansal
Jul 27, 2015

The number of triangles formed will be = ( 10 3 ) {10 \choose 3} − ( n 3 ) {n \choose 3}
⇒110=120− ( n 3 ) {n \choose 3}
⇒ ( n 3 ) {n \choose 3} =10
We know, ( 5 3 ) {5 \choose 3} =10
Hence, n=5

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