there are 5 people that can be seated in this staright line.
we used up one number, so we have 4 people to be seated.
3 people are remaining
2 people remaining
1 people remaining
5 = 120
this called 5 factorial
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
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
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
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!
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
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