Recent content by johnnyICON

awesome man, this is exactly how my prof wanted us to do it. thanks

here is a solution that I found, but uses a round table instead of a row. How many ways can 5 man and 7 women be seated at a round table with no 2 men next to each other? Solution. First place the women in 6!. Now there are 7C5 ways to pick 5 spots for the men so that they are not...

What I got was, mWmWmWmWW WmWmWmWmW WWmWmWmWm mWWmWmWmW WmWWmWmWm mWmWWmWmW WmWmWWmWm mWmWmWWmW WmWmWmWWm There are 9 in total. Each arrangement is 5!4!. Therefore 5!*4!*9 is the number of ways this can be done. Is this coorect?

I should of mentioed that each person is distinguishable from another. There are no two that are a like.

What if I were to up the ante of men and women to 4 and 5, respectively. During an exam, I shouldn't be writing all the possible permutations for the problem. I would get 4!5! for each arrangement, but how do I know how many arrangements there is going to be?

How many ways can 2 men and 3 women be seated in a row such that no 2 men are sitting beside each other? Now I have always had a problem with overthinking these kinds of questions. I'll usually write something down but then doubt myself. What I did was simply did 2! * 3!. 3 * 2 * 2 * 1 *...

I'm still fixated on this. :biggrin: Maybe if I make the Cs Zs instead?

"A sequence z0,z1,z2,... is defined by letting z0=3, and zk=(zk-1)2 for all integers k greater than equal to 1. Show that Ci=32i for i greater than or equal to 0." I e-mailed my professor, he said it is supposed to be Zi, not C... I don't know if that helps...

The very first sentence is straight from my textbook. I'm guessing Ci is just another way of representing Zk.

Here's how far I've gotten now, I'm trying to show that Ck+1=32k+1. By definition, Ck+1 = (Ck)2 = (32k)2 By the Induction Hypothesis = (32k(2)) = (32k+1) Is that correct?

Is this to be done using "Strong Induction" I was using basic mathematical induction.

A sequence z0,z1,z2,... is defined by letting z0=3, and zk=(zk-1)2 for all integers k greater than equal to 1. Show that Ci=32i for i greater than or equal to 0. I wasn't to clear on what it meant by this, so what I have is that I am trying to show that Zk = Ci. Is that correct? From...

Whoops, ignore my previous post. :D

Isn't it though? By the induction hypothesis I am assuming that P(n) is true, that is 3 divides n3-7k+3 where n is just k+1.

Ahhh, I didn't notice that when I was expanding out. The k's threw me off :( Question: You expanded -7(k+1). Where is the -7? [(k+1)^3-7k+3]-7 The equation within the brackets is divisible by 3, but -7 is not. I really like this approach because this is more of how I would try to solve the...