This year, you are helping organize your college’s career fest. There are 11 companies which are participating, and you have just enough room fit all of them. How many ways can you arrange the various firms, assuming…:
d) … Deutsche Bank representatives cancel, so you can give the additional space to one of the other companies?
We have 10 firms, which need to fill out 11 spots. Then, if we start filling up the room in some specific order, then there are going to be 10 options for who gets the first position. Since any firm can be given the additional space provided by DB’s withdrawal, then there are once again 10 options for the second spot. Then, there would be 9 different options for the third and so on. This results in having 10×10×9×8…×1=10×10!=36,288,000 many options to arrange the firms.
I dont understand this.
So, think about all the spots in the careers fest as different tables around a room. Hence, we have 11 objects and 10 firms and we have to fill them out in such a way that all 10 firms are placed somewhere.
Therefore, if we have filled out 10 of the spots with 10 different firms, then we have 10 choices for the last one right? So, for each of the ways we can arrange the 10 firms (P(10) = 10!), we have 10 ways of choosing who takes the 11-th table. Therefore, the answer is simply 10! * 10 = 36,288,000, so we have 36,288,000-many ways of arranging the room.
thanks a lot. I got it now.