How many different ways can 5 students stand in a row

Consider persons A, B, C, D, and E (5 persons). Each person is equally likely to be the first. That would be 5 possibilities (or 5 events for position 1).

Now consider that position 1 has been chosen. Position 2 can be filled be 1 of no more than 4 persons (because the first has already been associated with position 1). Hence, for the first 2 positions we have 5x4 (0r 20) possibilities. Continuing in this fashion for the remaining positions, we have 5x4x3x2x1 = 120 possible orderings (or permutations). Sometimes mathematics, scientists, and engineers write this as 5! (5 factorial).