Questions: A population consists of 14 observations. Fix the sample size as 4 , if order is not important, the total number of possible samples using simply random sampling method is (A) 24040 (B) 3632428800 (C) 1000 (D) 1001

Solution Steps

To determine the total number of possible samples when the order is not important, we need to calculate the number of combinations of 14 items taken 4 at a time. This can be done using the combination formula, which is given by \( C(n, k) = \frac{n!}{k!(n-k)!} \), where \( n \) is the total number of items, and \( k \) is the number of items to choose.

To find the total number of possible samples of size \( k = 4 \) from a population of size \( n = 14 \), we use the combination formula:

\[ C(n, k) = \frac{n!}{k!(n-k)!} \]

Substituting \( n = 14 \) and \( k = 4 \) into the formula gives:

\[ C(14, 4) = \frac{14!}{4!(14-4)!} = \frac{14!}{4! \cdot 10!} \]

Calculating the factorials, we find:

\[ C(14, 4) = \frac{14 \times 13 \times 12 \times 11}{4 \times 3 \times 2 \times 1} = \frac{24024}{24} = 1001 \]

Final Answer