induction & recursion: some collection of n sit in n consec.

[alichaudhary]

Again, a group of friends, which includes numerous engineers and non-engineers, are gathering for a social occasion. At one point, some collection of n of the partygoers will sit in n consecutive chairs. In this case, we always want two engineers sitting next to one another so they will have someone to talk shop to and we always want two non-engineers sitting next to one another. Also, each row will always begin with a non-engineer but may end with either type of individual. Let Sn be the number of ways of seating n people in these n chairs? Construct all possible arrangements and compute Sn for all values up to n = 5. Find and prove the correctness of a formula for Sn.

 

[Deleted member 4993]

Re: induction and recursion

Again, a group of friends, which includes numerous engineers and non-engineers, are
gathering for a social occasion. At one point, some collection of n of the partygoers will sit in n
consecutive chairs. In this case, we always want two engineers sitting next to one another so
they will have someone to talk shop to and we always want two non-engineers sitting next to one
another. Also, each row will always begin with a non-engineer but may end with either type of
individual. Let Sn be the number of ways of seating n people in these n chairs? Construct all
possible arrangements and compute Sn for all values up to n = 5. Find and prove the correctness
of a formula for Sn.

Please share with us your work/thoughts - indicating exactly where you are stuck - so that we know where to begin to help you.

Is this part of your homework - that you want us to do?

http://science.kennesaw.edu/~jdemaio/DM ... mework.pdf