Odds question

I just had a strange thing happen. We were playing cards with some friends of ours. We took a 52 card deck of cards and each person cut the deck and drew one card and kept it. After 4 cuts we revealed the cards and each one of us had a 5 of a different suit. What are the odds of this happening.
Thanks,
H

What do you think the odds are?

You have a deck of cards. You draw a five. What are the odds of drawing a five. There is one less five in the deck and one less card in the deck. You draw another five. What are the odds of drawing that five. There is now one less five in the deck and one less card in the deck. You draw another five. What are the odds of drawing that five? There is now one less five in the deck and one less card in the deck. You draw the final five. What are the odds of drawing one card from 49 cards remaining.

Now multiply them all together and what do you get? You multiply the odds together because you multiply probabilities together to get the total probability?

For example, if the odds of you figuring this out yourself is 25 percent and the odds of you reading this are 10 percent and the odds of you replying to this are fifty percent because you think I'm an a**hole, what are the odds that you will figure it out and reply back?

.25 x .10 x .5 = .0125 = 1.25 percent.

Back to the card example. For four FIVES:

4 / 52 * 3 / 51 * 2 / 50 * 1 / 49 = 24 / 6497400 = 270,725 : 1 or freakishly low.

But the odds of drawing a four of kind in any suit is 20,825 to 1, because the first card drawn will always be the first card to make four of a kind.

Many thanks for the solution.
H

Quote: boymimbo

4 / 52 * 3 / 51 * 2 / 50 * 1 / 49 = 24 / 6497400 = 270,725 : 1 or freakishly low.

It is actually the same for any particular four card combination, not just four fives. For example, having KS, 10C, 2C and 5H appear (in any order) is exactly the same. For some reason though drawing four fives seems a lot more surprising to us than some other random combination.