Question

A simple random sample of size 3 is drawn without replacement from a population of size 4. The possible number of samples is:

• A. 12
• B. 4
• C. 64
• D. 81

Hint:

Exam Tip:
For simple random sampling without replacement, the number of possible samples is \(\binom{N}{n}\).
For with replacement, it is \(N^n\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
We need to find the number of possible samples of size 3 from a population of size 4 without replacement.

Step 2: Key Formula or Approach:
The number of ways to choose \(n\) items from \(N\) items without replacement and without regard to order is given by combinations: \[ \binom{N}{n} = \frac{N!}{n!(N-n)!} \]

Step 3: Detailed Explanation:
Here, \(N = 4\), \(n = 3\): \[ \binom{4}{3} = \frac{4!}{3! \cdot 1!} = 4 \] So, there are 4 possible samples.

Step 4: Final Answer:
Therefore, option (B) is correct.