Answer to Question #279585 in Discrete Mathematics for Mark Yir

Question

There are 21 pupils in a grade 7 class. The class teacher has to choose eight of the pupils for a group that will visit Germany in three months time. In how many different ways can the teacher select pupils for the group ?

Answer 1

$n\raisebox{0.25em}{$C$}r=\frac{n!}{r!(n-r)!}$

$21\raisebox{0.25em}{$C$}8=\frac{21!}{8!(21-8)!}$

$21\raisebox{0.25em}{$C$}8=\frac{21!}{8!(13)!}=203490$

There are total 203,490 ways in which the teacher can select pupils for the group.