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)
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.
PLEASE tell me if this was helpful
and tell me how I can make my explanations better
Nice explanation :))
But shouldn't it be 25*24*3 instead of 25*25*24?
25*24 ways to choose 2 people, and 3 ways to then assign those 2 people.