Question

A club with 5 members is to choose three officers president vice president and secretary treasurer if each office is to be held by one person and no person can hold more than one office in how many ways can those offices be filled? Unlocked badge showing an astronaut’s boot touching down on the moon See what the community says and unlock a badge.

Answer 1

There are 60 different ways to fill the three distinct offices in the club using permutations, as no person can hold more than one office and there are 5 members available for these positions.

Step-by-step explanation:

The question is asking for the number of ways to fill three distinct positions (president, vice president, and secretary treasurer) with five members from a club, given that no person can hold more than one office. This is a problem of permutations where order matters, as the offices are distinct.

To calculate this, we consider the permutations of choosing 3 people from a group of 5 to fill the positions in order. For the first position, there are 5 possibilities (for any one of the club members to be chosen), for the second position there are 4 remaining possibilities (since one member is already chosen for the first position), and for the third position, there are 3 possibilities. Therefore, the total number of different ways to fill these positions is obtained by multiplying these numbers together:

The calculation is: 5 x 4 x 3 = 60 ways.

Thus, there are 60 different ways to fill the three offices in the club.