SOLUTION: Given three red balls, four green balls and five blue balls, what is the probability that when you arrange those balls, no blue balls are adjacent to each other? a. 1/99 b. 4/99

Algebra.Com
Question 1165592: Given three red balls, four green balls and five blue balls, what is the probability that when you arrange those balls, no blue balls
are adjacent to each other?
a. 1/99 b. 4/99 c. 5/99 d. 7/99

Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
3 red balls, 4 green balls and 5 blue balls,
We can arrange all the 7 non-blue balls in 7! ways.

Below, think of the 7 X's as representing the 7 non-blue balls.
Think of the 8 blanks as representing the 8 positions any 5 in 
which the 5 blue balls could be placed, between two non-blue
balls, left of the first non-blue ball or right of the last
non-blue ball.

_X_X_X_X_X_X_X_

For each of the 7! ways the non-blue balls could be placed,
there are P(8,5) ways to place the 5 blue balls.

That's (7∙6∙5∙4∙3∙2∙1)(8∙7∙6∙5∙4) = ways they could be placed
out of 12! ways the balls could be placed with no restrictions:


(7∙6∙5∙4∙3∙2∙1)(7∙6∙5∙4∙3)                     7
--------------------------- = after canceling ---
12∙11∙10∙9∙8∙7∙6∙5∙4∙3∙2∙1                     99

Edwin


RELATED QUESTIONS

If five balls are drawn from a bag containing six green balls, eight blue balls, and ten... (answered by Boreal)
Four Balls are selected without replacement from an urn containing three white balls and... (answered by stanbon)
You are going to draw 3 balls from the sack containing, 7 red balls,5 green balls, and 4... (answered by ikleyn)
If you are going to be drawing 3 balls from a sack containing 4 red balls, 3 green balls... (answered by ikleyn)
a container has 5 blue balls, 7 red balls, and 4 green balls. if 3 balls are drawn,... (answered by edjones)
An urn contains 4 red balls, 2 green balls, and 4 blue balls. If 10 balls are selected at (answered by VFBundy)
An urn contains 15 green, 10 blue, and 11 red balls. You take 3 balls out of the urn... (answered by Edwin McCravy,math_tutor2020)
Two urns each contain green balls and blue balls. Urn I contains five green balls and two (answered by stanbon)
Two urns each contain green balls and black balls. Urn 1 contains four green balls and... (answered by Simnepi)