Research in school

For particular research in high school, four pupils are selected from a class of 30 pupils. Calculate the number of all possible results of the selection and further calculate the number of all possible results if it depends on the order in which the students come to the interview.

Correct answer:

n₁ =  27405
n₂ =  657720

Step-by-step explanation:

$$\begin{gathered} C_4(30)=\left(\genfrac{}{}{0ex}{}{30}{4}\right)=\frac{30!}{4!(30-4)!}=\frac{30\cdot 29\cdot 28\cdot 27}{4\cdot 3\cdot 2\cdot 1}=27405 \\ {n}_1=\left(\genfrac{}{}{0ex}{}{30}{4}\right)=27405 \end{gathered}$$

$n_2=30\cdot 29\cdot 28\cdot 27=657720$

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