12.10 Solving Probability Problems by Using Combinations
A class consists of 19 girls and 15 boys. If 12 of the students are to be selected at
random, determine the probability that they are all girls.
The number of combinations of girls is 19C12.
The total number of combinations of children is 34C12
C12
To find the probability that they are all girls, the probability would be
34 C12
19
Ex 1 Determine the probability of being dealt 3 aces from a standard deck of 52
cards when 3 cards are dealt.
Ex 2 Of 80 people attending a dance, 28 have a college degree. If 4 people at the
dance are selected at random, determine the probability that each of the 4 has a
college degree.
Ex 3 Duc Tran’s wallet contains 8 bills of the following denominations: four $5 bills,
two $10 bills, one $20 bill, and one $50 bill. If Duc selects two bills at random,
determine the probability that he selects two $5 bills.
Ex 4 A full house in poker consists of three of one kind and two of another kind in
a five-card hand. For example, if a hand contains three kings and two 5’s, it is a
full house. If 5 cards are dealt at random from a standard deck of 52 cards,
without replacement, determine the probability of getting three kings and two 5’s.
Ex 5 An airline is given permission to fly 4 new routs of its choice. The airline is
considering 12 new routes: 4 routes in Florida, 5 routes in California, and 3 routes
in Texas. If the airline selects the 4 new routes at random from the 12
possibilities, determine the probability that:
a) 2 are in Florida and 2 are in Texas
b) 3 are in California and 1 is in Florida
c) 1 is in Florida, 1 is in California, and 2 are in Texas
d) at least one is in Texas.
12.10 Homework # 1 – 17 every other odd, 19 – 20, 27 – 30, 41