How many different simple random samples of size 4 from a population size 46

Question

How many different simple random samples of size 4 from a population size 46

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2 months 2021-07-30T08:20:12+00:00 1 Answers 5 views 0

This is one single number. The number is slightly larger than 163 thousand.

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Explanation:

Consider four slots labeled A,B,C,D

We have….

• 46 choices for slot A
• 45 choices for slot B
• 44 choices for slot C
• 43 choices for slot D

There’s a countdown going on (46,45,44,43) when filling up the slots. This countdown is because we cannot reselect any specific person for multiple slots at the same time.

If order mattered, then we’d have 46*45*44*43 = 3,916,440 permutations possible.

However, order doesn’t matter. For any group of 4 people, there are 4! = 4*3*2*1 = 24 ways to arrange them. So we must divide the previous result over 24 to get (3,916,440)/24 = 163,185

This means there are 163,185 different combinations and this is the number of possible samples of size 4 from a population of 46 people. The order of any sample doesn’t matter.