Question

how many different simple random samples of size 4 can be obtained from a population whose size is 43?
the number of simple random samples which can be obtained is
(type a whole number)

Explanation:

Step1: Use combination formula

The number of simple - random samples of size \(n\) from a population of size \(N\) is given by the combination formula \(C(N,n)=\frac{N!}{n!(N - n)!}\). Here \(N = 43\) and \(n=4\).

Step2: Calculate factorial values

We know that \(N!=N\times(N - 1)\times\cdots\times1\). So \(43! = 43\times42\times41\times40\times39!\), \(4! = 4\times3\times2\times1=24\), and \((43 - 4)!=39!\).
Then \(C(43,4)=\frac{43!}{4!(43 - 4)!}=\frac{43\times42\times41\times40\times39!}{24\times39!}\).

Step3: Simplify the expression

Cancel out the \(39!\) terms. Then \(\frac{43\times42\times41\times40}{24}\).
\(43\times42\times41\times40=(43)\times(42)\times(41)\times(40)=43\times1680\times41 = 43\times68880=2961840\).
\(\frac{2961840}{24}=123410\).

Answer:

\(123410\)