Question

There are 25 people who work in an office together. Five of these people are selectedto go together to the same conference in Orlando, Florida. How many ways can theychoose this team of five people to go to the conference?

Answer 1

ANSWER

53,130

EXPLANATION

There are 25 people and 5 have to be chosen from that group, with no specific order,

$_{25}C_5=\frac{25!}{(25-5)!5!}=\frac{25\times24\times23\times22\times21\times20!}{20!\cdot5\times4\times3\times2\times1}=\frac{25\times24\times23\times22\times21}{5\times4\times3\times2\times1}=53,130$

Hence, there are 53,130 ways to choose the five-people team.