Answer to Question #281737 in Discrete Mathematics for Neha

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.