Evaluate the given expression. $_9P_4$

• A. 24
• B. 3,024
• C. 15,120
• D. 362,880

Answer: (B)

Verified step by step guidance

1. Understand that 9P4 represents a permutation, which is the number of ways to arrange 4 items out of 9 distinct items.
2. The formula for permutations is given by: P(n, r) = n! / (n-r)!, where n is the total number of items, and r is the number of items to arrange.
3. Substitute the values into the formula: P(9, 4) = 9! / (9-4)!.
4. Calculate the factorials: 9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 and 5! = 5 × 4 × 3 × 2 × 1.
5. Simplify the expression by dividing 9! by 5! to find the number of permutations, which will give you the final result.