Evaluate the given expression. ${}_9{P}_4$

• A. 24
• B. 3024
• C. 15,120
• D. 362,880

Answer: (B)

Verified step by step guidance

1. Understand the notation: '9P4' represents a permutation, specifically the number of ways to arrange 4 items out of 9 distinct items.
2. Recall the formula for permutations: nPr = n! / (n-r)!, where n is the total number of items, and r is the number of items to arrange.
3. Apply the formula to '9P4': Calculate 9! (factorial of 9) and (9-4)! (factorial of 5), then divide 9! by 5!.
4. Calculate 9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 and 5! = 5 × 4 × 3 × 2 × 1.
5. Divide the result of 9! by the result of 5! to find the value of 9P4.