Combinatorics, Probability, & Binomial Theorem
Name:
1.
How many ways can 4 different books be arranged on a shelf?
2.
How many 4-digit positive even integers are there?
3.
How many different batting orders does a baseball team of nine players have if the pitcher
bats last?
4.
Determine if each situation is a permutation, combination, or neither.
a.)
classroom seating chart
b.)
a 3-digit lock combination
c.)
1st, 2nd, and 3rd chairs
d.)
a hand of five cards
5.
How many groups of 6 crayons can be selected from a box of 24 crayons?
6.
Consider a standard deck of 52 cards:
a.)
How many unique 5-card-hands can be drawn?
b.)
How many different 5-card-hands have all 5 cards of the same suit?
c.)
How many different 4-card-hands can have each card from a different suit?
7.
How many ways can 8 members of a family be seated side-by-side in a
movie theater if the father always gets the aisle seat?
8.
How many ways can 3 books be placed on a shelf chosen from a selection of 7 different books?
9.
From a group of 8 juniors and 10 seniors, a committee of five is to be formed. How many
committees can be formed under the given conditions?
a.)
all juniors
b.)
3 juniors, 2 seniors
c.)
1 junior, 4 seniors
d.)
all seniors
10.
How many ways can you choose 3 different pizza toppings from a list of 8?
11.
Three dice are tossed. What is the probability of rolling exactly 2 fives?
12.
For a play tryout, 10 students are reciting monologues. The order in which the students
perform is randomly selected.
a.)
What is the probability that the students audition in alphabetical order by last name?
b.)
What is the probability that 2 of your 4 friends trying out will be the first 2
performers?
13.
Six coins are tossed. What is the probability of getting 3 heads & 3 tails?
14.
The probability of Chris making a free throw is 2/3. If he shoots five times, what is the
probability of …?
a.)
exactly 4 shots made
15.
How many terms are in the expansion of (x-3y)19?
16.
9C5
17.
Find the 10th term in the expansion of (a-2b)14.
18.
Expand (2x+y)6 using the Binomial Theorem.
19.
Expand (x-3y)5 using the Binomial Theorem.
b.)
all shots made
(3x)4(-4)5 represents the ______ term in the expansion of the binomial _________ .