Ten employees of a company are to be assigned 10 different managerial posts, one to each post. in how many ways can these posts be filled?

This is a classic problem of permutations, where we are arranging 10 employees in 10 different positions. The number of ways to assign \(n\) employees to \(n\) posts is given by the formula for permutations:

\[
P(n) = n!
\]

Here, \(n = 10\), so the number of ways to assign 10 employees to 10 posts is:

\[
P(10) = 10!
\]

Now, let's calculate \(10!\):

\[
10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 3,628,800
\]

Thus, the number of ways to fill the 10 posts is **3,628,800**.

Would you like further details or explanations?

Here are 5 related questions to explore:
1. How does the solution change if some employees are ineligible for certain posts?
2. What if two employees are required to work in the same post together?
3. How many ways can 5 employees be selected from the 10 for top managerial roles?
4. How does the problem change if one employee is already assigned a specific post?
5. What if some posts are identical, making their assignments indistinguishable?

**Tip**: When dealing with permutation problems, remember that factorials grow very quickly!

Ten employees of a company are to be assigned 10 different managerial posts, one to each post. In how many ways can these posts be filled?

Discover how to solve a classic permutation problem where 10 employees are assigned to 10 different managerial posts. Learn how to calculate the number of ways using the factorial formula P(n) = n!. Suitable for high school students in Grades 9-12.

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