A sports club with 30 members wishes to pick a pres., vice-pres., sec, and trea. Assuming no person can hold two offices, in how many ways can the selection be made?

Question

anonymous · Answer

30*29*28*27. Of the 30 people, there are 30 different ways we can choose the president. Upon choosing the president, there are 29 different ways we can choose the vice-president. After choosing the president and vice-president, there are 28 different ways we can choose the sec. And then after that, 27 ways to choose the treasurer. So there are 30*29*28*27 ways the selection can be made.

Often times, these problems become easier if you work with easier numbers to understand the gist of the problem.
Instead of 30, make it 5. And instead of choosing four people, forget about the secretary and treasurer and choose 2. Make up some random names and choose the pres and vice pres

anonymous · Answer

Thank you. I thought that was the correct way to solve the problem, but the answer in the book is 24,360 not 30*29*28*27= 657720. I am hoping that the book is incorrect. I turn my assignment in tomorrow (well today) Thanks so much

anonymous · Answer

24360 = 30*29*28, so maybe they either forgot to multiply the 27 in, or they viewed the secretary and treasurer as the same person, ie. the secretary-treasurer.