Question

in how much ways can we order 6 objects so that 3 of them stay together

Answer 1

4! = 24 ways.

Answer 2

thnx tropical33 but can you pls explain me how u did that?

Answer 3

is it like 3! ways to combine the three objects that stay together, and then 4 and then 4!????

Answer 4

Six objects:

<A> <B> <C> <D> <E> <F>
Since 3 of them have to stay the same, we could write this as:
<A> <B> <C> <DEF>

At the first spot, there could be 4 objects (<A>, <B>, <C>, or <DEF>)
At the second spot, there can only be 3 objects, since one of them is at spot 1.
Contunue this and you get 24 ways.

Since <DEF> can also be written as <DFE> and such, you need to multiply 24 with 3!

24*3!=24*3*2=144 ways in total.

Yeah, I was wrong in my first post...

Answer 5

so it is 4!*3!

Answer 6

yes

Answer 7

ok, this makes sense, thanx a lot!!!!!!!!!!!
:D

Answer 8

that's what this whole website is about XD