Question

A,B,C and D is a quadilateral 3,4,5 and 6 points are marked on the sides of AB,BC,CD and DA respectively the number of triangles with vertices on the different sides is
A)270
B)342
C)292
D)302
​

Answer 1

The number of triangles with vertices on side AB,BC,CD=3C1×4C1×5C13C1×4C1×5C1

Similarly for other cases

∴∴ The total number of triangles =3C1×4C1×5C1+3C1×4C1×6C1+3C1×5C1×6C1+4C1×5C1×6C13C1×4C1×5C1+3C1×4C1×6C1+3C1×5C1×6C1+4C1×5C1×6C1

3C1=3!1!2!3C1=3!1!2!=3=3

4C1=4!1!3!4C1=4!1!3!=4=4

5C1=5!1!4!5C1=5!1!4!=5=5

6C1=6!1!5!6C1=6!1!5!=6=6

⇒3×4×5+3×4×6+3×5×6+4×5×6⇒3×4×5+3×4×6+3×5×6+4×5×6

⇒342


Hence the answer B is correct

Answer 2

B)342 is correct answer.