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