there are 35 members in a sports club. If an election is to be held to pick 4 officers; president, vice president, treasurer, and secretary, how many different lists of officers could result?
nPr
35!/(35-4)! = 35!/31!
35 * 34 * 33 * 32 * 31! / 31!
= 1256640
To find out the number of different lists of officers that could result, we need to calculate the number of ways we can select 4 members from a pool of 35.
We can solve this problem using the concept of combinations, specifically the combination formula.
The number of ways to choose k items from a set of n items is given by the combination formula:
C(n, k) = n! / (k!(n-k)!)
In this case, we want to choose 4 officers from a total of 35 members, so we can plug these values into the formula:
C(35, 4) = 35! / (4!(35-4)!)
Calculating this expression will give us the answer.