Hello, I'm on a page in my math book with all sorts of fun but slightly unusual 'using the strategies' problems. Most of the problems require specific

Hi Jedithious, it is great to see you back again.


"In how many different ways can you arrange 2 blue blocks and 2 red blocks in a straight line?"

I believe the answer is 4P4 / ( 2P2 * 2P2)

there is a nPr button on your calculator or

nPr = n! / (n-r)!
so 4P4 = 4! = 2 x 3 x 4 = 24 Thats how many ways 4 different coloured blocks can be arranged in line.
Then you have to divide by
2P2 because there are 2 red ones 2P2 = 2! / 0! = 2
and you have to divide by 2P2 again because there are 2 red blocks 2P2=2

So I think the answer is 24 / (2*2) = 6

These are the possible permutations RRBB,RBRB,RBBR,BRRB,BRBR,BBRR THAT IS IT!
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Now, lets look at how many ways you can order 4 different books in a more straight forward way.
There are 4 ways to choose the first book
now there are 3 books because there is one on the shelf already.
so there are 3 ways to choose the 2nd book
there are 2 ways to choose the 3rd book and
there is only 1 book left so there is only one way to choose it.
So, there are 4*3*2*1 ways of ordering the 4 books
this is 4!, it is also 4P4.
The P stands for permutations.
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Now you can do the other 2 by yourself I think
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You might find this interesting.
http://www.mathsisfun.com/combinatorics/combinations-permutations.html

Hello Melody, likewise.

This has always been an area of math I've lagged behind in, being for some reason daunted by it. But with your thorough explanation combined with that amazing link, that lag is suddenly no longer. I believe the answers to the other two are:

"In how many different ways can you arrange 9 blue blocks and 9 red blocks in a straight line?"
18! = 6,402,373,705,728,000
6,402,373,705,728,000/(9!) = 17,643,225,600
17,643,225,600/(9!) = 48,620

"In how many different ways can you arrange 25 blue blocks and 25 red blocks in a straight line?"
50! = 30,414,093,201,713,376,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
30,414,093,201,713,376,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000/(25!) = 1,960,781,468,160,819,281,929,913,523,584,869,531,669.8921948310508777
1,960,781,468,160,819,281,929,913,523,584,869,531,669.8921948310508777/(25!) = 126,410,606,437,751.9912453104638169556

Thank-you

P.S. That entire site is really delightful. I especially like the Pascals Triangle section.

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I also often find probability very difficult.
There are lots of helpful tools, like the ones I have shown you here, but as soon as the question is slightly different you need real insight to answer it correctly.
In other words, you can't just regurgitate the rules all the time like you can (to more of an extent) in many other areas of maths.
It has crossed my mind that we could have more general ongoing post/s that deal specifically with probability questions.
I might get up to it sometime. (I don't know if you would be able but maybe you would like to try)

Also, that mathisfun site appears to be really good. I often refer people to it. For all sorts of maths things. If you find stuff over there (or anywhere else) you can share it with us if you want to.
I like Pascal's triangle too. It is fun!

Now, let's look at your answers,

Jedithious:

This has always been an area of math I've lagged behind in, being for some reason daunted by it. But with your thorough explanation combined with that amazing link, that lag is suddenly no longer. I believe the answers to the other two are:

"In how many different ways can you arrange 9 blue blocks and 9 red blocks in a straight line?"
18! = 6,402,373,705,728,000
6,402,373,705,728,000/(9!) = 17,643,225,600
17,643,225,600/(9!) = 48,620 Totally correct.
I was a little confused at first because I didn't see that you had divided by 9! twice.
It would have looked better to someone trying to follow if you had done both at once, like this;
18!/(9!*9!) and then just gone to the answer.

"In how many different ways can you arrange 25 blue blocks and 25 red blocks in a straight line?"
50! = 30,414,093,201,713,376,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
30,414,093,201,713,376,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000/(25!) = 1,960,781,468,160,819,281,929,913,523,584,869,531,669.8921948310508777
1,960,781,468,160,819,281,929,913,523,584,869,531,669.8921948310508777/(25!) = 126,410,606,437,751.9912453104638169556
Now tell me please, how can you arrange 50 things in anything other than a WHOLE number of ways!
You answer doesn't make sense. It is very close to correct, I think your calculator did something funny, oh, I see, you used the calc on this site. It does some funny stuff sometimes.
There is an excellent online calculator that i suggest you use, I have already set it up with this answer.
http://www.wolframalpha.com/input/?i=50%21%2F%2825%21*25%21%29&lk=4&num=1&lk=4&num=1
Again a nicer presentation would just be
50!/(25!*25!)
Another thing, when you write really big, or really tiny, numbers it is a good idea to present them in scientific notation, For someone like me, who is used to it, it is much easier to interprete the size of the answer. (My eyes aren't great either so counting all the digits can be a problem.) You did put in the commas, that made it much easier.
Thank-you

P.S. That entire site is really delightful. I especially like the Pascals Triangle section.