You have 6 different trophies to arrange on the top shelf of a bookcase. How many ways are there to arrange the trophies?A.720B.120C.5040D.36

Step 1: Break Down the Problem

To find the number of ways to arrange 6 different trophies, we need to determine the number of permutations of 6 distinct items.

Step 2: Relevant Concepts

The formula for the number of permutations of $n$ distinct objects is given by: $n! = n \times (n-1) \times (n-2) \times \ldots \times 1$ In this case, $n = 6$.

Step 3: Analysis and Detail

We will calculate $6!$: $6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1$ Calculating step by step:

1. $6 \times 5 = 30$
2. $30 \times 4 = 120$
3. $120 \times 3 = 360$
4. $360 \times 2 = 720$
5. $720 \times 1 = 720$

Step 4: Verify and Summarize

We have confirmed that the calculation for $6!$ results in 720. Thus, the total number of ways to arrange the 6 different trophies is 720.

Final Answer

The number of ways to arrange the trophies is A. 720.