SOLUTION: Five white and four black balls are arranged in a row. What is the probability that the end balls are of different colors?

Question 339861: Five white and four black balls are arranged in a row. What is the probability that the end balls are of different colors?
Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
there are 9 total balls, so there are 9! total ways to arrange the balls
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of these, we are interested in when the end balls are of different colors, so tha leaves 7 balls in the middle (4 white and 3 black)which can be arranged in 7!
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the arrangements will be White*7!*Black or Black*7!*White
For White*7!*Black: that first white ball can be chosen in 5 different ways, and the last black ball can be chosen in 4 different ways,
so all together there are 5*7!*4=20*7! ways to do this
For Black*7!*White: that first black ball can be chosen in 4 different ways,
and the last white ball can be chose in 5 different ways
so all together there are 4*7!*5=20*7! ways to do this.
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So the probability is defined as #ways(White*7!*Black or Black*7!*White)/9!
=(20*7!+20*7!)/9!=40*7!/9!=40/(9*8)=5/9
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