Answer
The number of samples is 1,217,566,350.
Work Step by Step
The value of\[_{n}{{C}_{r}}\] can be calculated by
\[_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}\]
The population size is\[n=55\]
The sample size thatis required is 8, so\[r=8\]
Substitute the values in the above formula:
\[\begin{align}
& _{55}{{C}_{8}}=\frac{55!}{8!\left( 55-8 \right)!} \\
& =\frac{55!}{8!\,\cdot 47!} \\
& =\frac{55\times 54\times 53\times 52\times 51\times 50\times 49\times 48\times 47!}{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1\times 47!} \\
& =1,217,566,350
\end{align}\]
Hence, 1,217,566,350 samples can be obtained.
