# Research in school

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

Correct result:

n1 =  27405
n2 =  657720

#### Solution:

$C_{{ 4}}(30)=\dbinom{ 30}{ 4}=\dfrac{ 30! }{ 4!(30-4)!}=\dfrac{ 30 \cdot 29 \cdot 28 \cdot 27 } { 4 \cdot 3 \cdot 2 \cdot 1 }=27405 \ \\ \ \\ n_{1}={ { 30 } \choose 4 }=27405$
$n_{2}=30 \cdot \ 29 \cdot \ 28 \cdot \ 27=657720$

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