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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 option 'A'. Can you explain this answer?
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If from a population with 25 members, a random sample without replacem...
Random Sampling Without Replacement
Random sampling is a statistical technique used to select a representative sample from a larger population. In this case, we are asked to find the number of all possible random samples of size 2 that can be taken from a population of 25 members without replacement.
Formula for Combinations
The formula for combinations is used to calculate the number of ways that a sample of k elements can be selected from a set of n elements without regard to order. It is given by:
nCk = n! / (k! * (n - k)!)
where nCk represents the number of combinations of n things taken k at a time, n! represents the factorial of n, and k! represents the factorial of k.
Solution
Using the formula for combinations, we can calculate the number of all possible random samples of size 2 that can be taken from a population of 25 members without replacement as follows:
25C2 = 25! / (2! * (25 - 2)!) = 25 * 24 / 2 = 300
Therefore, the correct answer is option A, 300.
Random sampling is a statistical technique used to select a representative sample from a larger population. In this case, we are asked to find the number of all possible random samples of size 2 that can be taken from a population of 25 members without replacement.
Formula for Combinations
The formula for combinations is used to calculate the number of ways that a sample of k elements can be selected from a set of n elements without regard to order. It is given by:
nCk = n! / (k! * (n - k)!)
where nCk represents the number of combinations of n things taken k at a time, n! represents the factorial of n, and k! represents the factorial of k.
Solution
Using the formula for combinations, we can calculate the number of all possible random samples of size 2 that can be taken from a population of 25 members without replacement as follows:
25C2 = 25! / (2! * (25 - 2)!) = 25 * 24 / 2 = 300
Therefore, the correct answer is option A, 300.
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Community Answer
If from a population with 25 members, a random sample without replacem...
25C2=25!/23!2!=25*24/2=25*12=300
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