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: Idea:
Degrees of freedom equal the number of items minus the number of independent conditions that tie them together.

Step 2: Count items and conditions.
There are $n=58$ employees to place. The one condition is that all 58 must be seated, one on each seat, using up all the seats. That is 1 restriction.

Step 3: Subtract.
\[ 58 - 1 = 57 \]

Step 4: Sanity check with a small case.
Take 3 employees and 3 seats. The first has 3 choices, the second has 2 choices, the third has just 1 seat left. Only 2 of them decided freely, which is $3-1=2$. The same pattern gives $58-1=57$.

Step 5: Pick the option.
57 is option 2. The values 58, 59 and 58.5 do not match the rule $n-1$.

Final Answer:
The degrees of freedom are 57. \[ \boxed{57} \]