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  4. ABC is a triangle. 4, 5, 6 points are marked on the sides AB, BC, CA respectively, the number of triangles having vertices on different sides is

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Q. $ABC$ is a triangle. $4, 5, 6$ points are marked on the sides $AB, BC, CA$ respectively, the number of triangles having vertices on different sides is

Permutations and Combinations

Solution:

Required number of such triangles
$ = \,{}^{4}C_1 \times\,{}^{5}C_{1} \times\,{}^{6}C_{1}$
$ = 4 \times\, 5 \times\, 6$