To determine the number of ways the 5 parts of a clock can be assembled in any order, we are dealing with permutations, as the order of assembly matters.

The number of permutations for $n$ distinct objects is calculated as:

$n! = n \times (n-1) \times (n-2) \times \cdots \times 1$

Here, $n = 5$. Therefore:

$5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$

Thus, there are 120 different ways to assemble the 5 parts of the clock in any order.

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Additional Information:

• If the order did not matter (combination), the formula would be different. However, in this problem, order is crucial.
• The factorial growth in permutations explains why the number of orders increases so rapidly as the number of parts increases.

Would you like a detailed explanation of permutations and combinations or their applications in real-world problems?

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Follow-Up Questions:

1. How would the answer change if there were 6 parts instead of 5?
2. What is the difference between permutations and combinations in simple terms?
3. How can permutations be useful in project management or manufacturing efficiency studies?
4. What happens to the total permutations if two parts are indistinguishable?
5. How do factorials relate to probability problems in a similar context?

Tip:

Remember, permutations apply when order matters, and combinations apply when order does not matter. Always clarify the context to choose the correct formula!