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1
2
                                 this called 5 factorial
                    5 = 120
                 




                                 1 people remaining
                                    2 people remaining
                              3 people are remaining
we used up one number, so we have 4 people to be seated.
there are 5 people that can be seated in this staright line.
for every n1 and n2, there are 2 ways that 
there are 2 ways for n to be tossed.         q1 and q2 to be tossed and so that would 
                                             be 4.


                                            and for every q, there are 2 ways that d1 and d2 
                                            to be tossed and so that would be 8.




                                  now multiply all the numbers




                                                                                                3
The difference between Combinatories 
                                        and modeling is that combinatories 
                                        shows how many ways that can be done 
                                        and arrange items. the following 
                                        example show how to use it.
Mr. K gives us this example
there are 3 ways to wear the P1, P2 and P3, 
then there are P1 x P2 x P3 ways to do three 
things.




                                                                                4
= 40320
                          the basic idea is we have 6 student and 8 
                          possible position they can occupy.


we could solve this equation in the same way as the other equation by using 
the spaces and multiply all the numbers, but there is a shorter way. The 
factorial function on your calculator will perform this calculation for you!




                                                                               5
then we ask to solve this




                            ln is like log. This is  change of base law. 


                            first I expand the lnx and lny using 
     lnx2 + lny3÷ ln√z      the product law and by quotient 
                            law, I devide √z.

     2lnx + 3lny ÷ ½lnz     and the rest are self explanatory




                                                                            6
ln(x­1) + ln(x + 3)3 ÷ ln √(x2 + 2)



                                                        We can't expand ln(x­1) and ln(x+3) any 
                                                        further since logs are not distributive!
                                                                     ln(x­1) ≠ lnx­ln1, ln(x+3) ≠ lnx + ln3

                                                                          and the rest are for the review.......
this is a useful website to practice logarithms

                                     http://www.bmlc.ca/Pre­Calculus%20Math%2040s%20­%20Logarithms%20­%
                                     20Lesson%202.pdf




                                                                                                                   7
8
9
10

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Inverse1

  • 1. 1
  • 2. 2 this called 5 factorial 5 = 120   1 people remaining 2 people remaining 3 people are remaining we used up one number, so we have 4 people to be seated. there are 5 people that can be seated in this staright line.
  • 3. for every n1 and n2, there are 2 ways that  there are 2 ways for n to be tossed. q1 and q2 to be tossed and so that would  be 4. and for every q, there are 2 ways that d1 and d2  to be tossed and so that would be 8. now multiply all the numbers 3
  • 4. The difference between Combinatories  and modeling is that combinatories  shows how many ways that can be done  and arrange items. the following  example show how to use it. Mr. K gives us this example there are 3 ways to wear the P1, P2 and P3,  then there are P1 x P2 x P3 ways to do three  things. 4
  • 5. = 40320 the basic idea is we have 6 student and 8  possible position they can occupy. we could solve this equation in the same way as the other equation by using  the spaces and multiply all the numbers, but there is a shorter way. The  factorial function on your calculator will perform this calculation for you! 5
  • 6. then we ask to solve this ln is like log. This is  change of base law.  first I expand the lnx and lny using  lnx2 + lny3÷ ln√z the product law and by quotient  law, I devide √z. 2lnx + 3lny ÷ ½lnz and the rest are self explanatory 6
  • 7. ln(x­1) + ln(x + 3)3 ÷ ln √(x2 + 2) We can't expand ln(x­1) and ln(x+3) any  further since logs are not distributive!              ln(x­1) ≠ lnx­ln1, ln(x+3) ≠ lnx + ln3 and the rest are for the review....... this is a useful website to practice logarithms http://www.bmlc.ca/Pre­Calculus%20Math%2040s%20­%20Logarithms%20­% 20Lesson%202.pdf 7
  • 8. 8
  • 9. 9
  • 10. 10