A group of 5 employees and 3 leaders want to do a group meeting. They have decided to sit around a circular table such that all leaders will sit together. Find the number of ways in which employees can sit around a circular table such that all leaders will sit together.7201205,0402,520
Question
A group of 5 employees and 3 leaders want to do a group meeting. They have decided to sit around a circular table such that all leaders will sit together. Find the number of ways in which employees can sit around a circular table such that all leaders will sit together.7201205,0402,520
Solution
First, let's consider the 3 leaders as a single entity. So, we have 5 employees and 1 group of leaders, which makes 6 entities in total.
In a circular arrangement, the number of ways to arrange n entities is (n-1)!. So, the 6 entities (5 employees + 1 group of leaders) can be arranged in (6-1)!= 5! = 120 ways.
Now, within the group of leaders, they can arrange themselves in 3! = 6 ways.
So, the total number of arrangements is 120 * 6 = 720 ways.
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