as you can tell, I have problems with urn questions dealing with sampling with replacement. THe following question seems easier than the ones that I previously posted, but I decided to take the approach suggested by the answers in the previous posts to the following question, but I am getting answer greater than one. The question is:

There are 10 balls in a box: 5 white, 3 red and 2 black. We choose three balls at random with replacement. What is the probability that all 3 balls are of different colors?

a 0.03 b. 0.09 c. 0.18. d. 0.4 e. 0.84

My solution: (5/10)(3/10)(2/10)*3!, since for example WRB is different in arrangement than BRW. But this answer yields 180/100

I was able to initially get the answer by doing (5C1)(3C1)(2C1)/10^3 = 30/100 = 0.03 which matches answer a, but this method contradicts what has been previously posted regarding that this is a sampling with replacement problem, so I am a bit confused here.

Thank you

There are 10 balls in a box: 5 white, 3 red and 2 black. We choose three balls at random with replacement. What is the probability that all 3 balls are of different colors?

a 0.03 b. 0.09 c. 0.18. d. 0.4 e. 0.84

My solution: (5/10)(3/10)(2/10)*3!, since for example WRB is different in arrangement than BRW. But this answer yields 180/100

I was able to initially get the answer by doing (5C1)(3C1)(2C1)/10^3 = 30/100 = 0.03 which matches answer a, but this method contradicts what has been previously posted regarding that this is a sampling with replacement problem, so I am a bit confused here.

Thank you

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