Decks of Pinochle cards have a total of 48 cards and consist

Decks of Pinochle cards have a total of 48 cards and consist of 6 cards each of nines, tens, jacks, queens, kings, and aces with there being two of each suit of each denomination (for example, there are 2 aces each of diamonds, clubs, hearts, and spades for the total of 8 aces). Suppose that you are dealt a 12-card hand from a deck of Pinochle cards. What is the probability that:

a) you are dealt exactly 4 hearts?

b) you are dealt at most 2 aces?

Solution

a) total number of cards = 48,

total number of hearts = 12

probability of having the exactly 4 hearts = 12c4/48c12

b) probability with atmost 2 aces will incluse case 1) with no ace + 2) with one ace + 3)with two ace

1) with no ace = 40c12/48c12

2) with 1 ace = 8c1/48c1

3) with 2 aces = 8c2/48c2

add 1+2+3 and get the answer.