In a deck of cards with 52 cards we change clubs 8 with spades 10 and clubs 9 with spades jack from another deck of cards. What is the probability of getting two pairs if you draw 5 cards?
In a standard deck with 52 cards, the probability of getting two pairs could be calculated as follows:
We can determine the sample space by choosing 2 ranks of 13 existing ranks and then 2 suits of 4 existing suits for each pair of cards. Finally choose the last one among the remaining 11 ranks which can be done in 44 different ways. On the other hand the space is determined by choosing 5 cards among 52 cards.
Help me to find out how to determine the total number of possibilities in this case with a non-standard deck of cards.