Question

A club consists of 25 members, In how many different ways can they elect a president, vice-president, and secretary?

Answer 1

For ilusstration let us assume we have 3 boxes named president, vice-president, and secretary, now let us first select president then we have 25 ways to select vice president from , next let us choose vice-president now we have only 24 members from whom we can select because one person is already selected as a president , similarly for seceratary we have 23 ways this can be illustrated by following figure

So we have 25*24*23 = 13800 ways

Note : Here it is assumed a a person can not hold more than one position