### 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

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 B2! = AB seated next to eachother4! = 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 with48 = 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 with2 = 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

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 =)

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