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If from a population with 25 members, a random sample without replacement of 2 members is taken, the number of all such samples is
- a)300
- b)625
- c)50
- d)600
Correct answer is 'A'. Can you explain this answer?
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Calculation of Possible Samples
To determine the number of all possible samples of 2 members that can be taken from a population of 25 members, we use the formula for combinations:
nCr = n! / r!(n-r)!
Where n is the number of elements in the population, and r is the number of elements in the sample.
For this problem, n = 25 and r = 2, so we have:
25C2 = 25! / 2!(25-2)! = 25x24 / 2 = 300
Therefore, the number of all possible samples of 2 members that can be taken from a population of 25 members is 300.
Answer Explanation
Option A is the correct answer because it represents the number of all possible samples that can be taken from a population of 25 members. Option B is incorrect because it represents the number of possible arrangements of 2 members from a population of 25, which is a permutation and not a combination. Option C is incorrect because it represents the number of members in the population, not the number of possible samples. Option D is incorrect because it represents the number of possible samples with replacement, not without replacement.
To determine the number of all possible samples of 2 members that can be taken from a population of 25 members, we use the formula for combinations:
nCr = n! / r!(n-r)!
Where n is the number of elements in the population, and r is the number of elements in the sample.
For this problem, n = 25 and r = 2, so we have:
25C2 = 25! / 2!(25-2)! = 25x24 / 2 = 300
Therefore, the number of all possible samples of 2 members that can be taken from a population of 25 members is 300.
Answer Explanation
Option A is the correct answer because it represents the number of all possible samples that can be taken from a population of 25 members. Option B is incorrect because it represents the number of possible arrangements of 2 members from a population of 25, which is a permutation and not a combination. Option C is incorrect because it represents the number of members in the population, not the number of possible samples. Option D is incorrect because it represents the number of possible samples with replacement, not without replacement.
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If from a population with 25 members, a random sample without replacement of 2 members is taken, the number of all such samples isa)300b)625c)50d)600Correct answer is 'A'. Can you explain this answer?
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