Question

1. suzanne has 8 different plants to place in her window. how many ways can she arrange them?

Explanation:

Step1: Identify the problem type

This is a permutation problem since we are arranging distinct objects (8 different plants). The formula for permutations of \( n \) distinct objects is \( n! \) (n factorial), where \( n! = n \times (n - 1) \times (n - 2) \times \dots \times 1 \).

Step2: Apply the permutation formula

Here, \( n = 8 \), so we need to calculate \( 8! \).

$$ 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 $$

Calculating step by step:
\( 8 \times 7 = 56 \)
\( 56 \times 6 = 336 \)
\( 336 \times 5 = 1680 \)
\( 1680 \times 4 = 6720 \)
\( 6720 \times 3 = 20160 \)
\( 20160 \times 2 = 40320 \)
\( 40320 \times 1 = 40320 \)

Answer:

40320