Probability and Distribution Theory

How many different 5 card poker hands can be dealt from a deck of 52 cards f 52) 

There are = (52x51x51...xl)/[(5x4x3x2xl)(47x46x...xl)] = 2,598,960 possible hands. 

Compute the probability of being dealt 4 of a kind in a poker hand. 

There are 48(13) possible hands containing 4 of a kind and any of the remaining 48 cards. Thus, given the answer to the previous problem, the probability of being dealt one of these hands is 48(13)/2598960 =.00024, or less than one chance in 4000.  

Suppose a lottery ticket costs 1 per play. The game is played by drawing 6 numbers without replacement from the numbers 1 to 48. If you guess all six numbers, you win the prize. Now, suppose that N = the number of tickets sold and P = the size of the prize. N and P are related by 

---