permutation queston

[tuckletoe]

Source: Yahoo Answers
First decide if you want to place A on the ends or in the middle somewhere.
If on the ends (2 ways to do this): place B in one of the remaining 4 spots. Place C, D, F, and G in sequence in the remaining 4 spots, 3 spots, 2 spots, and 1 spot. This method gives 2*4*4*3*2*1 arrangements.

If you place A in the middle somewhere (4 ways to do this), place B in one of the remaining 3 spots. Place C, D, F, and G as before in the remaining 4 spots. This method gives 4*3*4*3*2*1 arrangements.

In total, you have 4*3*2*1 * (8 + 12) = 480 ways.

 

[ahmed t]

yes there alot of ways of answering this question choose which one is suitable for you

 

[tuckletoe]

Honestly, I didn't get the above thing properly.
I mean i am getting the answer about 432. You mind explaining Ahmed t?

 

[tuckletoe]

This reply was better. How many ways can Alice and Bob stand beside each other? Treat these two as a single unit. In doing so, we're left with only 5 units. So 5! = 120.

But there are two ways to arrange Alice and Bob as they stand beside each other, so the number of ways where Alice and Bob stand beside each other is 120 * 2 = 240.

How many ways are there to arrange them now?
= 6! - 240
= 720 - 240
= 480 (Answer)

 

[IgoforA]

answer is 480, 4! x 5P2. this is because, 4 persons can be arranged, so that means it's 4! and there are 5 ways that you can put that 2 persons in 4 of them. So its 5P2. True TRUE TRUE TRUE

 

[ahmed t]

yes we already established that long time ago

 

[mickysharif]

answer is 480, 4! x 5P2. this is because, 4 persons can be arranged, so that means it's 4! and there are 5 ways that you can put that 2 persons in 4 of them. So its 5P2. True TRUE TRUE TRUE

I don't get it how are there 5 ways we can put those 2 in the 4 people ...

if we have 4 people =
and two people who don't want to sit together :evil:

then

:evil: :evil:
:evil: :evil:
:evil: :evil:
:evil: :evil:
:evil: :evil:
:evil: :evil:
:evil: :evil: ... and so on. So how come there are 5 ways?

This reply was better. How many ways can Alice and Bob stand beside each other? Treat these two as a single unit. In doing so, we're left with only 5 units. So 5! = 120.

But there are two ways to arrange Alice and Bob as they stand beside each other, so the number of ways where Alice and Bob stand beside each other is 120 * 2 = 240.

How many ways are there to arrange them now?
= 6! - 240
= 720 - 240
= 480 (Answer)

This one makes the most sense to me. Thank you.

 

[memyself]

I don't get it how are there 5 ways we can put those 2 in the 4 people ...

if we have 4 people =
and two people who don't want to sit together :evil:

then

:evil: :evil:
:evil: :evil:
:evil: :evil:
:evil: :evil:
:evil: :evil:
:evil: :evil:
:evil: :evil: ... and so on. So how come there are 5 ways?

Haha, i like the notations ^^^
There aren't 5 ways, there are 5P2 = 20 ways