Question

A five-card hand is random dealt from a standard deck. We can classify a five-card hand into following possibilities: 1. Calculate the number possible five-card hands that are: Two denominations o Four of a kind: four cards from one denomination, one from another denomination o Full house: three cards from one denomination, two from another denomination . Three denominations o Three of a kind: three cards from one denomination, the other two from two different denomination Two pairs: two pairs and the fifth card is from a denomination other than the two pairs o .Four denominations: Exactly one pair: one pair and the other three cards are from three different denominations o . Five denominations: o No pairs: five cards from five different denominations. Show that the total counts in (1) is equal to C(52, 5).

please do all steps clearly!!!

Answer 1

The above is a problem of classical probability, here the no. of ways are the product of all the factors since there are no. of choices for each choices made earlier, so they are multiplied at the end. Lastly the no of choices for different cases add up to the total no of possible events since all the four cases are mutually exclusive and exhaustive cases and makes a partition.