Question

group of 30 people have been trained as astronauts to go on the first mission

to Mars. How many ways are there to select a crew of six people to go on this

mission (assuming that all crew members have the same job)?

Answer 1

n = total number of objects in the set = 30

r = number of choosing objects from the set = 6

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

$30\raisebox{0.25em}{$C$}6=\frac{30!}{6!(30-6)!}$

$30\raisebox{0.25em}{$C$}6=\frac{30!}{6!\times24!}$

$30\raisebox{0.25em}{$C$}6=\frac{30 \times29 \times28 \times27 \times26 \times25}{6 \times5 \times4 \times3 \times2 \times1}=593775$

There are total 593,775 ways to select a crew of six people from the group of 30 people to go on Mars mission.