If 11 cards are dealt from a 216 card deck (four 54 card decks, 2 jokers each), what is the probability of there being 2 of a kind (not including jokers)? Then, what is the probability of the next drawn card making 3 of a kind?
If 11 cards are dealt from a 216 card deck (four 54 card decks, 2 jokers each), what is the probability of there being 2 of a kind (not including jokers)? Then, what is the probability of the next drawn card making 3 of a kind?
Hello, c00ps!
I assume you mean exactly one 2-of-a-kind . . . and the other 9 cards do not match.If 11 cards are dealt from a 216 card deck (four 54 card decks, 2 jokers each),
what is the probability of there being 2 of a kind (not including jokers)?
Then, what is the probability of the next drawn card making 3 of a kind?
There are: . possible 11-card hands.
There are choices for the value of the pair.
Then there are: . ways to get that pair.
The other nine cards are 'singletons'.
There are: . choices for their values.
There are choices for each value.
Hence, the nine cards can be selected in: . ways.
Therefore: .
Hello, AGAIN, c00ps!
Here is the first part . . .
There are: . possible 11-card hands.More specifically, what's the probability there's AT LEAST one pair?
We will find the number of 11-card hands with no pairs.
There are two cases to consider.
(1) Eleven different values (no Joker).
There are: . choices for the 11 values.
There are: .16 choices for each value.
Hence, there are: . ways.
(2) One Joker and ten different valuies.
There are 8 ways to select a Joker.
There are: . choices for the 10 values.
There are 16 choices for each value.
Hence, there are: .
Thus, there are: . hands with no pairs.
So: .
Therefore: .