How many ways are possible to place (6) different balls in a row?

Correct answer: (720)

The direct answer is A: 720. There are six different balls, so every ball is distinguishable and the order matters. Fill the six places from left to right: 6 choices for the first place, then 5, 4, 3, 2 and 1. Thus the number is \(6\times5\times4\times3\times2\times1=6!=720\). Option A is correct because it gives 720. Option B, 36, is not the product of the decreasing choices. Option C, 120, equals \(5!\), as if only five objects were arranged. Option D, 60, also does not count all six-place arrangements. Remember: arranging all \(n\) different objects in a row gives \(n!\).