Question

what is the number of possible permutations of 9 objects taken 4 at a time?

a. 120

b. 126

c. 3,024

d. 362,880

Explanation:

Step1: Recall Permutation Formula

The formula for permutations of \( n \) objects taken \( r \) at a time is \( P(n, r)=\frac{n!}{(n - r)!} \). Here, \( n = 9 \) and \( r = 4 \).

Step2: Substitute Values into Formula

Substitute \( n = 9 \) and \( r = 4 \) into the formula: \( P(9, 4)=\frac{9!}{(9 - 4)!}=\frac{9!}{5!} \).

Step3: Simplify Factorials

Since \( n!=n\times(n - 1)\times\cdots\times1 \), \( 9! = 9\times8\times7\times6\times5! \). So, \( \frac{9!}{5!}=\frac{9\times8\times7\times6\times5!}{5!}=9\times8\times7\times6 \).

Step4: Calculate the Product

\( 9\times8 = 72 \), \( 72\times7 = 504 \), \( 504\times6 = 3024 \).

Answer:

C. 3,024