00:01
In how many ways can nine people be seated at a round table if a and b cannot be sitting next to each other? if we're at a round table with nine seats, and let's say we sat a at one, but it could be at any, there are nine options for person a to be sat.
00:25
But then person b could be sat at, there's six options, basically, any six, it's always going to be six choices for that one person after a has been sat.
00:51
And then you have seven more people to be sat.
00:54
And they can be sat anywhere.
00:57
So that would be seven factorial for the remainder of the people.
01:02
And seven times six, nine times six times seven factorial is 272 ,160.
01:21
In part b, c, d, and e must sit together.
01:27
If c, d, and e must sit together, we can first seat c in any of the nine chairs and then d and e on either side in the two of the eight remaining chairs.
01:41
After c and d, after cd and e are seated, we can then see the remaining six people in any order...