Thread: Probability Problem please help!

Please help! I'm not exactly sure where to start. I guess at first by figuring out all of the possible options and then is that it or what? But here's the problem: 6 red beads, 4 white beads, and 1 blue bead are placed in a line in random order. What is the probability that no two neighboring beads are the same color?

Originally Posted by sweeetcaroline

But here's the problem: 6 red beads, 4 white beads, and 1 blue bead are placed in a line in random order. What is the probability that no two neighboring beads are the same color?

Well your sample space is Now you need to find the event space. If we have positions, red can only be in one of the following ways:

_ R _ R _ R _ R _ R _R

R _ R _ R _ R _ R _R_

So we only have choices for red. Now no matter where we place white and blue they are not next to each other, so we have ways of placing the remaining beads.

That is

Thanks so much but why in the sample space is 3! included? Wouldn't it just be 6! x 4! x 1!?

_ _ _ _ _ _
We arranged the six red

_ _ _ _
Then the four white

_
Then the one blue.

Now think of each one of these color blocks as its own entity. Then we have 3! ways of arranging the 3 entities.

WAIT!

S=11!
Because we have 11! ways of arranging the 11 items.

Sorry about that.

Hello, sweeetcaroline!

Edit: Plato is absolutely right . . . *blush*

6 red beads, 4 white beads, and 1 blue bead are placed in a line in random order.
What is the probability that no two neighboring beads are the same color?

There are: . possible orders.



Place the 6 Red beads in a row, leaving a space between them.

. .


Place the Blue bead is any of the 5 spaces: . choices.


Drop the 4 White beads in the remaining 4 spaces: . way.


Hence, there are: . ways.


Therefore, the probability is: .

Originally Posted by sweeetcaroline

the problem: 6 red beads, 4 white beads, and 1 blue bead are placed in a line in random order. What is the probability that no two neighboring beads are the same color?

Can someone give me a line of these beads in which no two neighboring beads are the same color other than the five listed below?