Question

determine the number of permutations (arrangements) of the following.
11 objects taken 5 at a time

there are \\(\square\\) permutations of 11 objects taken 5 at a time.

Explanation:

Step1: Recall the permutation formula

The formula for permutations of \( n \) objects taken \( r \) at a time is \( P(n, r)=\frac{n!}{(n - r)!} \), where \( n!=n\times(n - 1)\times\cdots\times1 \). Here, \( n = 11 \) and \( r = 5 \).

Step2: Substitute values into the formula

Substitute \( n = 11 \) and \( r = 5 \) into the formula: \( P(11, 5)=\frac{11!}{(11 - 5)!}=\frac{11!}{6!} \).

Step3: Simplify the factorials

Since \( 11! = 11\times10\times9\times8\times7\times6! \), we can cancel out \( 6! \) in the numerator and denominator: \( \frac{11\times10\times9\times8\times7\times6!}{6!}=11\times10\times9\times8\times7 \).

Step4: Calculate the product

Calculate \( 11\times10\times9\times8\times7 \): \( 11\times10 = 110 \), \( 110\times9 = 990 \), \( 990\times8 = 7920 \), \( 7920\times7 = 55440 \).

Answer:

55440