probability of a horse winning a race. Lets suppose ten horses are participating in a race  and each horse has equal chance
of winning the race. I am required to find the following:  
(a) the probability that horse A wins the race followed by horse B.
(b) the probability that horse C becomes either first or second in the race.  
I know there are $10 \cdot 9 \cdot 8 $ ways of having first, second or third.  
Since each horse has an equal chance of winning, each has probability of 1/10.  Would I be right in saying that the probability that A wins followed by B is $\frac{1}{10}  \cdot \frac{1}{10} $?  
Is it okay if I do this for (b)? $\frac{1}{10} +\frac{1}{10} $?

The answer to A is 1/90 because of non replacement method. Horse A has 1/10 chance to be 1st and horse b would then be 1 of 9 with a chance to be 2nd. Multiply 1/10 times 1/9 gets 1/90th
The answer to b is different as its an addition problemas in he has a chance to be first and/or 2nd  so 1/10 plus 1/9...common denominator of 90 so 9/90 plus 10/90  or 19/90 chance. This is just a statistical question not a real question because percentages change based on post position, horse ability, jockey, trainer etc.
