Final answer:
The expression 16P4 represents the number of permutations of 16 items taken 4 at a time, which is calculated as 16 × 15 × 14 × 13, yielding a value of 43,680.
Step-by-step explanation:
The expression 16P4 is a mathematical notation that indicates a permutation, which is the number of ways to arrange 16 different items in groups of 4. To evaluate this, we use the formula for permutations: P(n, r) = n! / (n-r)!, where n is the total number of items, and r is the number of items to arrange.
Applying this formula, we have:
- n = 16
- r = 4
- 16P4 = 16! / (16-4)!
- 16P4 = 16! / 12!
- 16P4 = (16 × 15 × 14 × 13 × 12!) / 12!
- 16P4 = 16 × 15 × 14 × 13
- 16P4 = 43680
Therefore, the value of 16P4 is 43,680.