How many distinct permutations of 4 distinct items are possible?

• A. 8
• B. 12
• C. 24
• D. 6

Answer: (C)

When order matters, count how many ways to arrange all four items. For the first position you can pick any of the four items, for the second position any of the remaining three, the third position from the remaining two, and the last position is fixed by the remaining item. Multiply these choices: 4 × 3 × 2 × 1 = 24. This is 4 factorial, the standard count for all possible orderings of four distinct items. The other numbers would correspond to scenarios with fewer options or without regard to order, but with four distinct items where every arrangement counts, there are 24 distinct permutations.