A club with 35 members is to select five officers (president, vice president, secretary, treasurer, and historian). In how many ways can this be done?
35 choose 5 = C(35,5) = 35!/(5!(35-5)!)
To find the number of ways to select the officers, we need to consider the number of choices for each position.
For the president position, there are 35 possible choices since any member can become the president.
For the vice president position, there are 34 remaining members to choose from since we cannot select the same person as the president.
Similarly, for the positions of the secretary, treasurer, and historian, there are 33, 32, and 31 choices respectively.
To calculate the total number of ways to select the officers, we need to multiply the number of choices for each position:
35 choices for the president × 34 choices for the vice president × 33 choices for the secretary × 32 choices for the treasurer × 31 choices for the historian.
Using multiplication, we can calculate:
35 × 34 × 33 × 32 × 31 = 17,297,760.
Therefore, there are 17,297,760 ways to select the five officers from a club of 35 members.