fitz Probability question (1 Viewer)

[ToO LaZy ^*]

in how many ways can 4 physics books and 3 maths books be arranged on a shelf if a selection is made from 6 different physics books and 5 different maths books? in how many of these arrangements are the physics books together?

the answer is 756000; 86400

can anyone tell me how they got that plz?

 

[mojako]

6c4*5c3*7!

6p4*5c3*4!

 

[ToO LaZy ^*]

"6p4*5c3*4!"..could you explain how you got that?

 

[mojako]

"6p4*5c3*4!"..could you explain how you got that?

well since u said I dont think I can explain it
its just one of those inspection techniques.
u need to learn how to do inspection.
its one of those secrets to success in the HSC maths course.

http://www.google.com.au/search?hl=en&q=inspection&meta=

 

[ToO LaZy ^*]

ok..what was ⁿP_r again?

argh crap..didnt work..

 

[mojako]

ok..what was ⁿP_r again?

argh crap..didnt work..

hahaha...

look at the magical ⁿP_r :
ⁿP_r

 

[ToO LaZy ^*]

nah dude, seriously..can you help me out?

 

[tempco]

The 4! is used since you're considering the Physics books as one "book" since they have to go together, and the other 3 Maths books as separate books. So instead of 7! for 7 different books, it's 4!

 

[jumb]

And the p is used because the order taht those 4 books are in is importan.... for some reason.

 

[jumb]

ok..what was ⁿP_r again?

argh crap..didnt work..

use < > brackets

ⁿP_r

 

[ToO LaZy ^*]

And the p is used because the order taht those 4 books are in is importan.... for some reason.

yeah..that's what i didn't get..
oh well.
thx anyway

 

[Jase]

Do we really need to learn this?

Inspection

 

[lizbon]

isnt it 6c4*5c3*(4!)^2, since we're treating the physics bks as just a sub group within the total, which is 4!*4!

 

[mojako]

yeah..that's what i didn't get..
oh well.
thx anyway

if u meant u still dont know why order is important:

you're arranging 7 books on the shelf...
placing book A on the very left near the door is different from placing it on the other side...

6c4*5c3*7!:
6C4 to select 4 physics books to be picked up and put in a temporary box before they're moved to the shelf (hence order doesn't matter)
5C3 to select 3 maths books
7! to order them on the shelf (since you have 7 books)

6p4*5c3*4! or probably, to better follow the above pattern, 6C4*5C3*4!*4!:

6C4*5C3*4!*4!
the 6C4 and 5C3 are to choose the books as before
the first 4! is to order the 4 physics on the shelf
the second 4! is to order these four items: (physics books) (maths 1) (maths 2) (maths 3)

6p4*5c3*4!:
we can also consider the physics as being separate.
6P4 to choose the physics books and order them within themselves, then they're tied together with a piece of strong indestructible rope and put in the temporary box
5C3 to choose 3 maths books to be put in the temporary box
4! to order the four things in the box, one is likely to be heavier than the other 3 because it's 4 books tied with a piece of indestructible rope

 

[mojako]

Do we really need to learn this?

Inspection

if you want to get 100% tomorrow, YES!
I've got a lot of stuff to catch up on...
these numerous inspection techniques are crazy...

 

[ToO LaZy ^*]

OHHHHHHHHHHHHHHHHHH11!!..now i get it.
thx love.

 

[tempco]

_nP^r

Funky.

 

[ToO LaZy ^*]

a few more questions:
five cards are drawn at random from a pack of 52 playing cards. what is the probability that they are all from the same suit?

and...

a bag contains 5 red balls and 4 white balls. 3 balls are drawn without replacement. find the prob. of drawing at least 2 red balls..

yes i suck at probability..

 

[Archman]

12/51*11/50*10/49*9/48
and
((5*4*4)/(9*8*7)) * 3 + (5*4*3)/(9*8*7)

 

[ToO LaZy ^*]

ok
cheers
sgdgdgr