Question

There are seven members in a club. In how many different ways can a president, vice president, and treasurer be chosen?
Answer

24

840

120

210

Answer 1

here it means that out of seven persons you need to choose any three of them for each post
for choosing the first one you have 7 options and for choosing the second one you have
6 options and for the last person you have only 5 options
hence the required number of ways are 7*6*5=210 ways

note if you have to merely chose any three of them (i.e without assigning any designation)it could have been done in C(7,3)=35 ways but in the above question u have to assign posts too to each of them ...