SamplingMCQMTP June 24 Series IIQuestion 2792 of 295
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If from a population with 25 members, a random sample without replacement of 5 members is taken, the number of all such samples is

Options

A300
B625
C50
D600
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Correct Answer

✅ Option a — 300

All Options:

  • A300
  • B625
  • C50
  • D600

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Detailed Solution & Explanation

Note: There is a typographical error in the question due to PDF parsing, where the sample size of '2' was parsed as '5'. In the standard textbook problem, a random sample of 2 members is taken from a population of 25. Using the combination formula for selection without replacement where order does not matter: Number of samples=(Nk)=(252)\text{Number of samples} = \binom{N}{k} = \binom{25}{2} Number of samples=25×242×1=300\text{Number of samples} = \frac{25 \times 24}{2 \times 1} = 300 This corresponds to Option A. (If the literal value 5 is used, the number of samples is (255)=53,130\displaystyle \binom{25}{5} = 53,130, which is not in the options. This confirms the correct sample size is 2.) Hence, **Option A** is the correct answer.

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