two tracks are parallel . the first track has 6 checkpoints and the second one has 10 checkpoints . in how many ways can the 6 checkpoints of first track be joined with the 10 checkpoints of the second to form a triangle ?
to make a triangle , you need 2 checkpoints from one track and 1 from the other . you can not have all 3 from the same track since then the points will be in a line ( assuming straight line of track ) you select 2 checkpoints from the first track and one from the second or two from the second track and one from the first . 6 c 2 * 10 c 1 + 10 c 2 * 6 c 1 = 150 + 270 = 420 answer ( e )
add(multiply(divide(divide(factorial(10), factorial(subtract(10, const_2))), factorial(const_2)), divide(factorial(6), factorial(subtract(6, const_1)))), multiply(divide(factorial(10), factorial(subtract(const_10, const_1))), divide(divide(factorial(6), const_2), factorial(subtract(6, const_2)))))