Which of the following statements are true? Justify your answers. This means that if you think a statement is false, give a short proof or an example that shows it is false. If it is true, give a short proof ...

Lost your password? Please enter your email address. You will receive a link and will create a new password via email.

Please briefly explain why you feel this question should be reported.

Please briefly explain why you feel this answer should be reported.

Please briefly explain why you feel this user should be reported.

To evaluate the statement "The total number of all possible samples of size 3 without replacement from a population of size 7 is 21," we need to use the concept of combinations. Combination Formula The number of ways to choose a sample of size \(r\) from a population of size \(n\) without replacemenRead more

To evaluate the statement “The total number of all possible samples of size 3 without replacement from a population of size 7 is 21,” we need to use the concept of combinations.

## Combination Formula

The number of ways to choose a sample of size \(r\) from a population of size \(n\) without replacement is given by the combination formula:

\[

C(n, r) = \frac{n!}{r!(n-r)!}

\]

where \(n!\) denotes the factorial of \(n\).

## Application to the Statement

In this case, we have a population size \(n = 7\) and a sample size \(r = 3\). Plugging these values into the combination formula:

\[

C(7, 3) = \frac{7!}{3!(7-3)!} = \frac{7!}{3! \times 4!} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35

\]

## Conclusion

The statement “The total number of all possible samples of size 3 without replacement from a population of size 7 is 21” is

See lessfalse. The correct number of samples is 35.