getting a specific hand X times in Y hands

[pirlouit]

I would like to calculate the probability of that.

Let's say that probability of having a specific hand by the river in a hold'em game is P.

I'd say that the probability of having 2 in a row would be P*P.
3 times in a row would be P*P*P

Then what is the probability of having this hand X times among Y hands ?
Spontaneously, I would say Y*(P^X), but I'm not sure.

After a few thinking, I'd rather say : YCX*(P^X)

Is that right ?