A club of 10 members is to select 3 officers (president, vice-president and secretary). In how many ways can they do this?
A club of 10 members is to select a committee of 3 persons. In how many ways can they do this?
is it 1000
720
To find the number of ways the club can select 3 officers from the 10 members, we can use the concept of permutations.
For the president position, there are 10 members to choose from. Once the president is selected, there are 9 remaining members to choose from for the vice-president position. Finally, once both the president and vice-president are chosen, there are 8 remaining members to choose from for the secretary position.
Therefore, the total number of ways to select the 3 officers is:
10 * 9 * 8 = 720.
So, there are 720 ways the club can select the 3 officers.
For selecting a committee of 3 persons from the 10 members, we can again use the concept of permutations.
The number of ways to choose a committee of 3 persons can be calculated as:
10! / (3! * (10-3)!) = 120.
This formula represents the combination of 10 members taken 3 at a time, which is equal to 120.
Therefore, there are 120 ways the club can select a committee of 3 persons.