SOLUTION: The problem goes like this: There are 10 detergent brands that are to be ranked. Determine the probability that a.) brand A is ranked first and b.) that brand A is in the top 3

Question 1000955: The problem goes like this:
There are 10 detergent brands that are to be ranked. Determine the probability that a.) brand A is ranked first and b.) that brand A is in the top 3 brands.
I know that the answer to the first is .10, because each of the brands have 1/10 probability of ranking first. I'm not sure how to solve for b.)
An explanation would be great with the solution.
Found 2 solutions by Boreal, stanbon:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Probability that A is in the top three brands.
It may occur first, second, or third.
(1/10) for the first, or 0.10
(9/10)*(1/9) for the second, which is 0.10. It can't be first, but all the others can be.
(9/10)(8/9)(1/8) for the third, which is 72/720 or 0.10. The first is 9/10, the second is 8/9, because there are nine left and 8 non-As to choose from
The probability is 0.3.
The assumption is that all brands have an equal chance of being chosen.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The problem goes like this:
There are 10 detergent brands that are to be ranked. Determine the probability that
a.) brand A is ranked first and
b.) that brand A is in the top 3 brands.

I know that the answer to the first is .10, because each of the brands have 1/10 probability of ranking first.
I'm not sure how to solve for b.)
An explanation would be great with the solution.
# of ways for brand A to be in the top 3:: 3*9!
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# of random arrangements; 10!
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P(A in top 3) = 3*9!/10! = 3/10
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Cheers,
Stan H.s

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