## Calculating the Odds of Winning

I'm trying to calculate the odds of winning a promitional event. The game is as follows:

There will be 50 envelopes each with a poker card in it.
The envelopes will only have 10, J, Q, K, A cards in them (no 9's or below)
There will be cards from all four suits (clubs, diamonds, hearts, spades)

What are the odds that if someone were allowed to draw 5 cards, that they would draw a royal flush (A, K, Q, J, 10 of the same suit).

Now, what if the contest were run 7 times...what are the odds that someone would draw a Royal Flush in those 7 attempts?

Now, what if the game were set up so that there was only one suit that could possibly draw out the five necessary cards, and in that suit there was only one card each. So, for example, the Jacks were removed from all of the suits except for spades (so that there was zero chance for a Royal Flush in anything but Spades) and for Spades, there was only one each of the 10,J,Q,K,A.

What would the odds be of someone drawing out a Royal Flush then?

What if it were done 7 times, then what would the odds be?