hard permutations question (1 Viewer)

[Michaelmoo]

This wont work sorry, just like gurmies said
"Your method fails to acknowledge that 135792468 is a possibility...as is something like, say, 821345796"

I might be wrong but:
[4^5 + 3^5 + 2^5 + 1^5]*4! = 31,200

Chose a place for 1, there are 4 spots as you have to allow room for all the potential spacings. Then there are 4 spots for 3 and so on (hence 4^5)...but I think my logic breaks down as for each 1-4 extra spaces you allow it creates even MORE 1-4 cases.

There are similar alphabetical order questions in Cambridge 3U using words, none of which I have solved either.

Um. My method does acknowledge the fact that you can have all those different possibilities. If it didn't, I would've multiplied by 1 instead of 9C5. I chose all the possible combinations of 5 from the 9 places. I dno how ur thinking about it. But that includes scenarios such as OOOOOEEEE, OEOOEEOOE, EEOOOOOEE etc.

Ur method is completely wrong lol. You've created an excess of positions.

Tim and lolokay seem to have got the same answer as me from a different approach though.

 

[emmcyclopedia]

i agree with lolokay - i got 9!/5!.

i haven't read other people solution yet,

but is it 4!x5x6x7x8x9 / 5!

yeah, i knew it was simpler than what i did (although it only took like 10 seconds)

4!x5x6x7x8x9/5! is exactly the same as 9!/5! ? lol

 

[addikaye03]

4!x5x6x7x8x9/5! is exactly the same as 9!/5! ? lol

Yeah, but the way Timothy done it was different than the way lolokay did it, you can tell by his working. Not that either are more correct, we realise they're the same thing. Timothy just released that there was an easier way at solving the question. Well done to both though

The answer is 3024 ways.

 

[leapordfist]

so which is the correct answer?!?!?!? lol
thanks alot for the replies though guys,
this is supposed to be an easy question, it was in my exam
which is part of that independent schools exam thingi, which are generally quite easy...

 

[kevinthoang]

Well since your 5 odd numbers are in increasing order, I will place them first and there is only one way to do this
13579
Then you have to place your 4 even numbers so for example, there are 6 possible spaces to place 2 and then 7 for the number 4, etc.
giving you 6*7*8*9 giving you 3024

This is right... hopefully =]