If I choose four cards from a standard $52$-card deck, with replacement, what is the probability that I will end up with one card from each suit?
Since there are $4$ suits, wouldn't the probability just be $\displaystyle\left({\frac{1}{4}}\right)^4?$ I feel like I'm missing something here, any help? Thanks in advance.
The probability of four different suits is the probability that the second card is not the same suit as the first and the third card is a different suit than the first two and the fourth card is the last suit: $$\frac{39}{52}\cdot\frac{26}{52}\cdot\frac{13}{52}=\frac{3}{4}\cdot\frac{2}{4}\cdot\frac{1}{4}=\frac{3}{32}$$