Melody

You look for a square number that goes into 320.

I see 16

$$\\\sqrt{320}=\sqrt{16}\times \sqrt 20\\\\
\sqrt{320}=4\times \sqrt {20}\\\\
\sqrt{320}=4\times\sqrt{4}\times \sqrt 5\\\\
\sqrt{320}=4\times 2\times \sqrt 5\\\\
\sqrt{320}=8 \sqrt 5\\\\$$

$$x=\sqrt{256}$$

Yes it would be very difficult.  Maybe you select the book off the shelf but then read it off a kindle.  That way the selected book would never leave the shelf and you could select 4 of the same book.  You could almost recite it after reading it 4 times. 

Then your probability would be correct. :)

I like your book shelves. :)

Hi Nauseated,

I do not believe your answer is correct.

Binomial expansion are only used when the trials are independent. :)

Excellent

now see if you can write out all those permutations.

there are exactly 10 of them 😉

27x33

There are lots of "tricks"

If I was doing that in my head I'd say

3x20=60

3×7=21

So.  3×27=60+21=81

30×27=810

So 33x27=810+81=891

Yes great.

5!      Is 5 factorial and it means

1x2x3x4x5

so what would  5!/(2!×3!) equal?

Why don't you try a little one.

Say

AABBB

how many permutations can you make with those letters?  Just copy my technique.

Can you name them all?

It does seem like an awful lot but I think that it is correct. :)