Question

Consider a office having seating capacity of 58 employees and all of them are to be seated in such a way that an employee can sit on any available vacant seat . What will be the degree of freedom?

• A. 58
• B. 57
• C. 59
• D. 58.5

Hint:

With n items to place, the last one has no free choice. So the degrees of freedom are n minus 1.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Degrees of freedom are the number of values that can be chosen freely before the rest get fixed by a condition. In this seating problem the condition is that every employee gets exactly one seat.

Step 2: Count the free choices.
The first employee can pick any of the 58 seats. The second can pick from the 57 that remain, and so on. Each choice is free until only one employee and one seat are left.

Step 3: The last employee.
When 57 employees are seated, exactly one seat is left. The 58th employee has no choice at all. So that last placement is not free.

Step 4: Apply the rule.
\[ \text{degrees of freedom} = n - 1 = 58 - 1 = 57 \]

Step 5: Check the other options.
58 would count the last employee, who has no choice. 59 is more than the number of employees. 58.5 is not possible, because degrees of freedom are whole numbers. So only 57 fits.

Final Answer:
The degrees of freedom are 57, which is option 2. \[ \boxed{57} \]