Suppose we have a set {1,.....,r} where r = 1, and we select three numbers independently and randomly from the set. Find the probability that
a) the 3 nos are different (when r = 3)
b) the 3 nos are same (when r = 1)
c) exactly 2 nos are same (when r = 2)

Question

Suppose we have a set {1,.....,r} where r >= 1, and we select three numbers independently and randomly from the set. Find the probability that 
a) the 3 nos are different (when r >= 3)
b) the 3 nos are same (when r >= 1)
c) exactly 2 nos are same (when r >= 2)

anonymous · Answer

I need help on this asap

anonymous · Answer

a) you pick some number, and it is unique with probability 1, then second number different from first has probability $\frac{r-1}{r}$ and third number different from first two has probability $\frac{r-2}{r}$ so the probability that all three are distinct is $\frac{r-1}{r}\times \frac{r-2}{r}$