Three members of a club will be selected to serve as officers. The first person selected will be president, the second person will be vice-president and the third will be secretary/treasurer. How many ways can these officers be selected if there are 30 club members?
nPr
30!/(30-3)! = 30!/27!
=24360
To find the number of ways the officers can be selected, we need to determine the number of choices for each position.
For the first position of president, there are 30 possible choices since any of the 30 club members can be selected.
For the second position of vice-president, there are 29 remaining choices after the president has been selected. This is because one person has already been chosen, leaving 29 club members to choose from.
For the third position of secretary/treasurer, there are 28 choices remaining after the president and vice-president have been selected.
To find the total number of ways the officers can be selected, we multiply the number of choices for each position:
30 choices for the president × 29 choices for the vice-president × 28 choices for the secretary/treasurer = 24,360 ways
Therefore, there are 24,360 ways the officers can be selected from the 30 club members.