NDA2016MathematicsPermutation and CombinationActual
Out of 15 points in a plane, n points are in the same straight line. 445 triangles can be formed by joining these points. What is the value of n ?
Options
- A3
- B4
- C5
- D6
Correct answer
C. 5
Step-by-step solution
Here, ¹⁵ C₃- ^n C₃=445 aligned & ^n C₃= 15! 3!12! -445 & ^ n C ₃=10 & ^3 C ₃=1 ; ^4 C ₃=4 ; ^5 C ₃=10 & n =5 aligned