What are the odds? (20 cards, 10 of them red and 10 black)

[jayme]

My daughter and I came across this seemingly unlikely situation and we're trying to figure out what the odds were of this happening. We had 20 cards, 10 of them red and 10 black. They're shuffled well. Then we randomly picked out 10 cards and all were red. What are the odds of this?

 

[mmm4444bot]

Hello. Has this situation arisen from schoolwork? If so, then has your daughter already learned how to determine the odds that the first drawn card is red?
[imath]\;[/imath]

 

[pka]

My daughter and I came across this seemingly unlikely situation and we're trying to figure out what the odds were of this happening. We had 20 cards, 10 of them red and 10 black. They're shuffled well. Then we randomly picked out 10 cards and all were red. What are the odds of this?

@jayme: Does your daughter understand the difference in probability & odds?
Drawing ten cards from that deck, there are [imath]\dbinom{20}{10}=184756[/imath] possible hands.
How many of those are all red cards?