Will somebody double check my math on this

[TRBNGR]

Im looking to determine the probability that given a deck of X cards, Y of them the same (by rank[4] or suit[13]) what is the probability that at least one has been chosen after Z cards are dealt. To make it concrete lets use the discreet example of -- 'What is the probability that at least 1 heart has been chosen after 10 cards are dealt from a standard deck?'

Step 1)
1 - Probability of No hearts Dealt After 10 Cards

Step 2)
Probability of No hearts Dealt After 10 Cards =
Ways to choose 10 cards without a heart / Total Ways to Choose 10 cards

Step 3)
1 - [c(42, 10) / c(52,10)]


Is this correct?

and would the general formula be

1 - [c(X-Y,Z)/c(X,Z)]?

[Cobra]

[ QUOTE ]
Step 1)
1 - Probability of No hearts Dealt After 10 Cards

[/ QUOTE ]

Correct

[ QUOTE ]
Probability of No hearts Dealt After 10 Cards =
Ways to choose 10 cards without a heart / Total Ways to Choose 10 cards

[/ QUOTE ]

Correct

[ QUOTE ]
1 - [c(42, 10) / c(52,10)]


[/ QUOTE ]

Incorrect. It needs to be 1-[c(39,10)/c(52,10)]
You have to choose the ten cards from the 39 that are not hearts.

Cobra

[TRBNGR]

LoL! Thank you... Just like me to get the 'higher' level math correct and butcher the arthimetic.