Our club has 25 members, and wishes to pick a president, secretary, and treasurer. In how many ways can we choose the officers, if individual members are allowed to hold 2 but not all 3 offices?

(if you give an answer always explain it, answers mean nothing compared to an understanding of the problem)

viola May 1, 2021

#1**+2 **

Okay I will try to explain this as best as I can.

If the members were not allowed to hold two positions, the answer would be **25*24*23**.

This is because there are **25 **people who can run for the first spot, and **24 **people who can run for the second, because

the first spot would be taken, and there will only be **24** people availible for the second. Same goes with the **23**. (I hope I am not making this confusing.)

But **because** we can't do that, we have to try something else. If a member can hold two spots, the number of spots will be

**25*25*24**. This accomendates for two spots and allows a member to have two positions.** 25*25*24** is equal to **15,000**

So there are** 15,000 combinations**.

mathisopandcool May 2, 2021

#2**+2 **

PLEASE tell me if this was helpful

and tell me how I can make my explanations better

:)

mathisopandcool
May 2, 2021