Chapter 13 Combinatorics and Probability
13.1 and 13.2 Combinations and Permutations
Ex 1: There are 3 shirts and 5 pairs of pants.
a. How many outfits can you make with these shirts and pants?
b. What if there are also 4 pairs of shoes along with the 3 shirts and 5 pairs of pants? Find the number of
outfits.
Choosing Multiple Things from a Category
Ex 2: Find the number of possible pizzas using the following topping options if the pizza has…
Meat: Pepperoni, Anchovies, Sausage, Canadian Bacon, Bacon
Veggies: Bell Pepper, Basil, Onion, Pineapple, Olives, Jalapeños
Cheeses: Mozzarella, Feta, Goat Cheese, Parmesan
a. 1 of each kind of topping
b. 1 meat, 3 veggies, 2 cheese toppings
c. 2 meats, 2 veggies, and 1 cheese
Ex 3: Find the number of arrangements of letters for each word
a. BACON
b. MISSISSIPPI
c. CONNECTICUT
Circular Arrangement
Ex 4: There are 5 people sitting around a circular table. How many arrangements of people can be placed at
the table?
Ex 5: Thirteen children are to be seated on horses on a merry-go-round for which the attendant collects
tickets, beginning with the brown horse.
a. Is the arrangement of the children on the ride a linear or circular permutation?
b. How many possible arrangements of children relative to the brown horse are there?
13.3 Probability and Odds
Ex 1: There are 7 red, 2 purple, 5 yellow, 3 orange and 4 green skittles in a bag. Find each probability or odds.
a. Pick one.
P(purple)
b. Odds (a purple)
c. Grab 4 at random.
P(2 red, yellow, orange)
d. Grab 4 at random.
Odds (1 red, 1 purple, 2 green)
Ex 2: A box of 60 baseball cards contains 8 cards with print errors on them. If 5 cards are selected at random,
what is the probability that all 5 have print errors?
Ex 3: Twelve male and 16 female students have been selected as equal qualifiers for 6 college scholarships. If
the awarded recipients are to be chosen at random, what are the odds that 3 will be male and 3 will be
female.
Ex 4: Four male and 2 female students have been selected as equal qualifiers for 2 college scholarships. If the
awarded recipients are to be chosen at random, what is the probability that one will be male and one will be
female? What are the odds?
Complements
Ex 4: A production line supervisor knows that 4 of the 100 whatnots manufactured during a particular shift
are defective. If 8 of the whatnots are chosen at random, what is the probability that at least 1 of them is
defective?
13.4 and 13.5 Probability or Compound Events and Binomial Theorem and Probability
Ex 1: A six-sided die is thrown. Find each probability.
a. P(roll a 5 or 2)
b. Roll Twice. P(4 and 4)
Ex 2: There are 7 green, 4 yellow and 2 pink crayons in a box. Two are chosen randomly. Find each
probability.
a. P(both are green, with replacement)
b. P(Yellow then pink, without replacement)
c. P(2 different colors, without replacement)
Ex 3: A card will be randomly chosen from a standard deck of playing cards. Find each odds.
a. P(club or Q)
b. P(Q or K)
Ex 4: There are 10 students and 7 teachers in a group to be interviewed by the local paper. The writer wants
to interview 5 people at the same time. Find the probability that at most 2 are teachers.
Binomial Experiments/Probability
Ex 5: There are 10 multiple choice questions on a test. Each questions has 4 choices. Ted did not study, so he
guessed on all 10 questions. Find each probability. (Wrong = success)
a. P(gets all wrong)
b. P(miss 6 problems)
13.5 Conditional Probability
Ex 1: There are 15 baseball, 20 football and 12 basketball players. Of them, 7 basketball players, 14 football
players and 5 basketball players are on the JV team, which the others are on Varsity. Find each probability
when a person is chosen.
a. Probability that the chosen person is a football player given he is on the varsity team.
b. P(JV Team | Basketball)
c. P(Baseball | Varsity)
Ex 2: There are 3 true or false questions on a survey. Find each probability.
a. Exactly 2 of your answers are true, given there’s at least 1 true answer.
b. P(Exactly 1 F | at most 2 F)
Ex 3: 4 digit codes are created using 1, 2, 3, 4. No digits repeat. Find the probability the code ends with 23
given the 4 digit code is odd.