Question

At the head table at a banquet are seated two senators, two governors, and three mayors. Find the number of ways in which these seven people can be seated under the conditions described: A mayor is at each end and the senators are in consecutive seats

Answer 1

hi

Answer 2

lots of applications of the counting principle
two choices for mayor

Answer 3

ok so how will u do the senators?

Answer 4

oh i read it wrong, sorry

Answer 5

lets back up a bit

Answer 6

label the seats 1 to 7
then senators can be in seats
2, 3
3, 4
4, 5
5, 6

and they can switch chairs between them, so there are 8 possibilities for the senators

Answer 7

seat number 1 and 7 must contain mayors, so there are \(3\times 2=6\) choices for seat 1 and 7

Answer 8

then you have 3 chairs left to fill , and 3 people left to sit, so they are \(3\times 2=6\) choices for the remaining 3 chairs

Answer 9

multiply all these choices together, and unless i screwed up you get the right answer

Answer 10

... the answer is 12

Answer 11

@Mertsj
?

Answer 12

I do not see how the answer can only be 12.

Answer 13

Are you sure it is 12?

Answer 14

well i guess order doesn't matter i nthnis case

Answer 15

yea its 12... hey can u just help me on this question?

how many committees of four can be chosen from twelve students?

how many of these will include a given student?

how many will exclude a given student?

Answer 16

It's a comination problem so 12 choose 4