Permutations and Combinations

Question

Please help me answer the following questions! I'm stuck and keep getting the wrong answer!
1. Find the number of six-letter arrangements that can be made from the letters in the word SYDNEY.

2. Seven people are to seated at a round table.

a. How many seating arrangements are possible?
b.Two people, Kevin and Jill, refuse to sit next to each other. How many seating arrangements are then possible?

Answer 1

1.  6!/2!  (division by 2! because of the duplicate Ys)

 

2a. 6! (because the first person merely establishes the beginning of the seatings--everyone else is arranged relative to that first person)  (in linear arrangements, it matters whether one is positioned at beginning or end; in circular arrangements, that concept does not exist)

 

2b.  I'll let you work this out..essentially you have to root out all possible Kevin/Jill immediate neighbor possibilities.