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To find the number of ways $5$ managers can be assigned to $5$ different branches, you can use the concept of permutations.

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Identify and classify polygons

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Q. To find the number of ways

5

managers can be assigned to

5

different branches, you can use the concept of permutations.

Permutations Definition: We're dealing with permutations since the order matters for assigning managers to branches.
Permutations Formula: The formula for permutations is $P(n, r) = \frac{n!}{(n-r)!}$ where $n$ is the total number of items to choose from, and $r$ is the number of items to choose.
Identifying Parameters: Here, $n = r = 5$ because we have $5$ managers and $5$ branches.
Calculate $P(5, 5)$ : So, we calculate $P(5, 5) = \frac{5!}{(5-5)!} = \frac{5!}{0!}$ .
Handling $0!$ : Remember that $0!$ is equal to $1$ .
Calculate $5!$ : Now, calculate $5!$ which is $5 \times 4 \times 3 \times 2 \times 1 = 120$ .
Final Result: So, $P(5, 5) = \frac{120}{1} = 120$ .

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