If a club consists of 10 members, how many different arrangements of president, vice-president, and secretary are possible?
There are 10 choices for the first position (president), 9 remaining choices for the second position (vice-president), and 8 remaining choices for the third position (secretary). Therefore, the total number of arrangements is:
10 x 9 x 8 = 720
There are 720 different arrangements of president, vice-president, and secretary possible in a club with 10 members.
To find the number of different arrangements of president, vice-president, and secretary in a club of 10 members, we need to consider the concept of permutations.
A permutation is an arrangement of objects in a specific order. In this case, we have 10 members, and we need to arrange them in different positions for president, vice-president, and secretary.
The first position, president, can be filled by any of the 10 members. Once the president is chosen, there are 9 remaining members for the vice-president position. Finally, for the secretary position, there are 8 remaining members.
To find the total number of arrangements, we multiply the number of options for each position:
10 (options for president) * 9 (options for vice-president) * 8 (options for secretary) = 720
Therefore, there are 720 different arrangements of president, vice-president, and secretary in a club of 10 members.