November 30, 2006

SCRIBE POST NOVEMBER 17

Hey everyone its Gerald. I understand my scribe post is pretty late and i'm very sorry.
To get things started Mr. K put some questions on the board for us to do.

HOW MANY WAYS CAN 5 PEOPLE (A,B,C,D,E) SIT IN A ROW IF A MUST:

A) SIT NEXT TO B
B) NOT SIT NEXT TO B
C) SIT TO THE LEFT OF B BUT NOT NECESSARILY NEXT TO B

SOLUTION:

A) 4!2! = 48 ways to be seated in a row if A must be seated next to B

2! = AB seated next to eachother
4! = C,D,E,AB = since AB must be seated together

B) 5! = 120

120 - 48 = 72 ways to be seated not next to B

5! = all ways they can be seated regardless who they sit with
48 = the ways AB are seated together

C) 5! divided by 2 = 60 ways A sit next to be but not necessarily next to B

5! = all ways they can be seated regardless who they sit with
2 = A sitted to the left of B

IN HOW MANY WAYS CAN 5 PEOPLE SIT AT A ROUND TABLE

the formula for this is (n-1)!

(5-1)! = 4!
4! = 24 ways 5 people can sit around a table

MATH DICTIONARY NOTES:

CIRCULAR PERMUTATIONS

the number of ordered arrangements that can be made of "n" objects in a circle is given by:

(n-1)!

example: how many ways can 6 people be arranged around a circular table?
(6-1)! = 5!
5! = 120 ways 6 people can be arranged around a circular table

SPECIAL CASE: a bracelet is a circle that can be flipped over. The number of arrangements that can be made of object on a bracelet is:

(n-1)! divided by 2

example: how many different bracelets can be made using 5 different coloured beads?
(5-1)! divided by 2 = 4! divded 2
24 divided by 2 = 12 ways a bracelet is made using 5 beads

thanks and sorry once again. I hope everyone did good on the recent test we just had. See everyone next class. Good night and goodbye =)