How many different simple random samples of size 4 can be obtained from a population whose size is 47 ?
The number of simple random samples which can be obtained is
(Type a whole number.)

To find the number of different simple random samples of size 4 from a population of size 47, you can use the combination formula, which is given by . Here, and .

Calculating this:

So, the number of different simple random samples of size 4 from a population of size 47 is 123,410.

Now, let’s dig a little deeper into the world of sampling!

Sampling strategies have been pivotal throughout history. Consider the 1936 US presidential election when The Literary Digest inaccurately predicted a victory for Alf Landon over Franklin D. Roosevelt based on a flawed sampling method. This event highlighted the critical importance of proper sampling techniques and set the stage for more rigorous statistical methods that followed.

In real-world applications, sampling is central to fields such as market research, healthcare, and social sciences. For instance, when launching a new product, companies might survey a diverse sample of potential customers to assess reaction before a full launch. This method helps them gather valuable insights while minimizing costs and time.