Almost Xtreme and Mxy...
Which is the probability of getting a royal flush if you pick up only 5 cards and considering your deck is complete (52)?
I never said any suit in particular, so your answer is lacking something.
hmm. I don't want to think so deep into this, but I'm not sure if that's the right answer. Taking 2 years of probability, I found that the answer isn't always so easy.
The first card can be any suit, A, K, Q, J, or 10. The following cards' suit is determine by this first card's suit. So I think it is
20/52 * 4/51 * 3/50 * 2/49 * 1/48 = 1/649740.
I'm not sure on this answer either.
Good job Goalie. Indeed, one way to see this problem is considering you have 4 suits available, and once you pick up one suit, the probability decreases drastically.
It is indeed 1/649740
Other ways to look at this is as follows...
1) Understanding the relationship between the mentioned two probabilities
Probability of getting royal flush of 1 suit (Ps Prob. suit)
Ps = 1/2598960
Probability of getting royal flush considering 4 suits (Pt Prob total)
Pt = 4Ps = 1/649740
2) Knowing how to use combination
Combination is the number of possibilities of taking n elements out of k elements, considering that order is not important and there is no substitution of elements, being k>0 and 0<=n<=k. It is noted as (consider both parenthesis joined as one)
( k ) k!
= --------- I'll use kCn for notation
( n ) n!(k-n)!
Now, considering that there is no substitution when drawing the cards, and that order does not matter (Prs, Prh, Prc, Prd Prob Royal Flush of spades, hearts, clubs and diamonds)
5C5
Pt = -------- * 4 = Prs+Prh+Prc+Prd
52C5
So, the probability can be seen as the possibilities of drawing the 5 cards of the royal flush, divided by the possibilities of drawing any 5 cards out of the deck, times the number of suits available.
Your turn Goalie!!!