From a standard 52 card deck, how many 6-card hands have exactly 4 spades and 2 hearts?
The # of ways we can choose 6 random cards out of a pack of 52 cards is 52C6. Now the possibility that out of these randomly selected cards 4 are spades is 13C4. similarly the possibility that 2 cards selected randomly are hearts is 13C2. The required possibility, i.e a random hand of 6 card contains exactly 4 spades and 2 hearts is given by the product: 52C6x13C4x13C2. // Note: The additional factor here, i.e. 52C6 justifies the fact that the 6 cards are randomly selected out of a pack of 52, otherwise it would mean as if we were just drawing spades and hearts from their respective sets of 13 each which were seperated from other sets.
