Question

How many samples of size n=2 can be drawn from a population size of 10?

A. 54
B. 45
C. 20
D. 5


I NEED HELP PLEASE THANK YOU


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Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

How many samples of size n = 2 can be drawn from a population size of 10

A. 54

B. 45

C. 20

D. 5

EVALUATION

Size of the population = 10

Size of sample = 2

Hence the required number of samples of size n = 2 can be drawn from a population size of 10

$\sf = {}^{10} C_2$

$\displaystyle \sf{ = \frac{10!}{2!(10 - 2)!} }$

$\displaystyle \sf{ = \frac{10!}{2! \: 8!} }$

$\displaystyle \sf{ = \frac{10 \times 9 \times 8!}{2! \: 8!} }$

$\displaystyle \sf{ = \frac{10 \times 9 }{2! } }$

$\displaystyle \sf{ = \frac{10 \times 9 }{2 } }$

$\displaystyle \sf{ =45}$

FINAL ANSWER

Hence the correct option is B. 45

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Answer 2

No.of samples can be drawn from a Population size of 10 is

= ¹⁰C₂

= (10!)/2(10 - 2)!

= 10!/2!.8!

= 10•9•8!/2!•8!

= 10•9/2!

= 10•9/2

= 90/2

= 45