Question

Random samples with size 5 are drawn from the population containing the values 26, 32, 41, 50, 58, and 63.

Determine the number of possible samples with size 5.

Answer 1

Consider two situations: samples without replacement (order of numbers does not matter) and samples with replacement(order of numbers matters). In case we consider samples without replacement (order of numbers does not matter), we get $6$ different samples. We have to determine, which element to exclude (from $6$ numbers) to receive samples of size $5$. For samples with replacement(order of elements matters) we receive $6^5$ elements. We used multiplication principle of combinatorics. Namely, we have $5$ empty places and we have $6$ choices for each place.

Answer: there are $6$ different samples without replacement(order of numbers does not matter) and $6^5$ samples with replacement(order of numbers matters).