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A population comprises of 5 units. The total number of all possible samples each of size 2 units that can be drawn from the population with replacement is:
- a)100
- b)15
- c)125
- d)25
Correct answer is option 'D'. Can you explain this answer?
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A population comprises of 5 units. The total number of all possible sa...
To find the total number of all possible samples of size 2 units that can be drawn from a population of 5 units with replacement, we can use the combinations formula.
The combinations formula is given by:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of units in the population and r is the sample size.
In this case, n = 5 and r = 2.
So, plugging in the values into the combinations formula, we have:
C(5, 2) = 5! / (2!(5-2)!)
Simplifying further:
C(5, 2) = 5! / (2! * 3!)
Now, let's calculate the factorial values:
5! = 5 * 4 * 3 * 2 * 1 = 120
2! = 2 * 1 = 2
3! = 3 * 2 * 1 = 6
Substituting these values back into the combinations formula:
C(5, 2) = 120 / (2 * 6) = 120 / 12 = 10
Therefore, the total number of all possible samples of size 2 units that can be drawn from the population with replacement is 10.
However, since we are given multiple-choice options, we need to check which option matches our result.
The options given are:
a) 100
b) 15
c) 125
d) 25
Since none of the options match our result of 10, we can conclude that the correct answer is not among the given options.
The combinations formula is given by:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of units in the population and r is the sample size.
In this case, n = 5 and r = 2.
So, plugging in the values into the combinations formula, we have:
C(5, 2) = 5! / (2!(5-2)!)
Simplifying further:
C(5, 2) = 5! / (2! * 3!)
Now, let's calculate the factorial values:
5! = 5 * 4 * 3 * 2 * 1 = 120
2! = 2 * 1 = 2
3! = 3 * 2 * 1 = 6
Substituting these values back into the combinations formula:
C(5, 2) = 120 / (2 * 6) = 120 / 12 = 10
Therefore, the total number of all possible samples of size 2 units that can be drawn from the population with replacement is 10.
However, since we are given multiple-choice options, we need to check which option matches our result.
The options given are:
a) 100
b) 15
c) 125
d) 25
Since none of the options match our result of 10, we can conclude that the correct answer is not among the given options.
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Community Answer
A population comprises of 5 units. The total number of all possible sa...
Size is 2 hence 5 square is = 25
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A population comprises of 5 units. The total number of all possible samples each of size 2 units that can be drawn from the population with replacement is:a)100b)15c)125d)25Correct answer is option 'D'. Can you explain this answer?
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