Intergration of Trig

Thanks again

You are welcome.

Mr M can you please quickly explain why -ln(e+1) + ln2 = -ln(e+1)/2)
and not ln(2/(e+1)) ?

Mr M can you please quickly explain why -ln(e+1) + ln2 = -ln((e+1)/2)
and not ln(2/(e+1)) ?

They are the same.

$\displaystyle \ln \frac{a}{b}=-\ln \frac{b}{a}$

Use your knowledge of the laws of logarithms to figure out why.

Thanks, Im really struggling with permutations and combinations.
For example this question

In how many ways can a committee of four men and four women be seated in a row if
a) they can sit in any positions - which is 8!
b) no one is seated next to a person of the same sex? < I dont get this?

Think of it as 4 double seats containing MF instead of 8 single seats.

Don't keep adding to this thread - if you have new questions about a different topic make a new thread.

Will do, can you please help me finish this and I will create a new thread from now on

so 4! = 24 options theres something missing, this is a hard topic

Well at the moment you have every man paired with a particular woman ...

I was moving the figures around and I got the right answer but it doesnt apply to any other questions so I think on the off chance its right lol

I did

4! x (4! x 2!) = 1152

So you have 4! ways to arrange the double seats

But there are 4! male/female pairings

And the rows can be populated in 2 different ways

MF MF MF MF or FM FM FM FM

Are you saying the Calculation above it right?

So for this question ill go through your step
six people are going to travel in a six-seater minibus but only 3 of them can drive. In how many different ways can they seat themselves?

So If i treat the people who can drive as one

D CCC

D= Drive C= Cant drive

4! ways to arrange the seats
but there are 3 in who can drive so 3!
and the seats can be populated in 2!

so 4! x (6! x 2!) I dont get this at all

That is very wrong. The other two people who are capable of driving can sit in any of the passenger seats.

How many ways to do it are there if only 1 person of the 6 can drive?

5! who cant drive = 120 options

But 3 people can drive so what is the answer ...