# Permutations and Combinations Questions and Answers

Algebra

Permutations and CombinationsWhat is the probability of rolling 6 on a fair number cube and flipping a coin and getting tails? Write your answer as a percent rounded to the tenths place. Do not include the percent symbol.

Algebra

Permutations and CombinationsIf A and B are mutually exclusive, and if P(A) = 32% and P(B) = 35%, what is P(A or B)?
P(A or B)=

Algebra

Permutations and CombinationsS and T are mutually exclusive events. Find P(S or T).
P(S)=5/8
P(T) = 1/8
P(S or T) =d to three decimal places as needed)

Algebra

Permutations and CombinationsTelephone numbers are preceded by a 3-digit area code (e.g. 437). In the following
questions, any digit from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9) can be used unless otherwise stated.
How many area codes are possible if:
a. the first digit must be 1?
b. the third digit must not be 4?
c. the second and third digits must be the same?
d. neither 1 nor 2 must be used?

Algebra

Permutations and CombinationsS and T are mutually exclusive events. Find P(S or T). Write your answer as a fraction in simplest form (a/b).
P(S) = 3/5, P(T) = 1/3

Algebra

Permutations and CombinationsIn a group of 11 students, there are 6 females and 5 males
How many different 4-member committees are possible if there are no restrictions?
How many different 4-member committees are possible there must be exactly 2 girls?
How many different 4-member committees are possible there must be at least 1 girl?
Determine the probability that a 4-member committee chosen at random from this
group will consist of at least 1 females. Write your answer as a percent.___%

Algebra

Permutations and CombinationsA ski resort has 3 chair lifts, each with access to 6 ski trails. Explain how you can find the number of possible outcomes when choosing a chair lift and a ski trail without making a list, a tree diagram, or table.

Algebra

Permutations and CombinationsFind an equation of the line having the given slope and containing the given point.
Slope 3/4 through (-4,4)

Algebra

Permutations and CombinationsA class rolled number cubes. Their results are shown in the table. What is the experimental probability of rolling each number?

Algebra

Permutations and CombinationsA group of 30 students from your school is part of the audience for a TV game show. The total number of people in the audience is 150. What is the theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots?

Algebra

Permutations and CombinationsBaby Ethan wants to arrange 9 blocks in a row. How many different arrangements can he make?

Algebra

Permutations and CombinationsAssume that 3 customers arrive and order different appetizers to share from a choice of 12 appetizers.
a. Does this problem involve permutations or combinations?
b. Why?
c. In how many possible ways can this be done?

Algebra

Permutations and CombinationsA jar contains 30 red marbles, 50 blue marbles, and 20 white marbles. You pick one marble from the jar at random. Find the theoretical probability.
a. P(red)
b. P(not white)

Algebra

Permutations and CombinationsA monk crossbred plants, which can have purple or white flowers, and obtained 502 plants with white flowers and 351 plants with purple flowers. Find the experimental probability that a plant had each type of flower.

Algebra

Permutations and CombinationsTo create an entry code, you must first choose 3 letters and then, 4 single-digit numbers. How many different entry codes can you create?

Algebra

Permutations and Combinationsexplain in words why three forces must lie in the same plane when they are acting on an object in equilibrium

Algebra

Permutations and CombinationsYou want to be able to withdraw $40,000 each year for 30 years. Your account earns 6% interest.
a) How much do you need in your account at the beginning?
b) How much total money will you pull out of the account?
c) How much of that money is interest?

Algebra

Permutations and CombinationsMr. Anderson put $1000 into an account that earns 4.5% annual interest. The interest is compounded annually and there are no withdrawals. How much money will be in the account at the end of 30 years? Round to the nearest cent.

Algebra

Permutations and CombinationsUse synthetic division and the Remainder Theorem to find the indicated function value.
f(x)=x4 + 4x³ + 3x²-3x-7; f(6)

Algebra

Permutations and CombinationsSuppose Alice encrypted an existing English word using Hill cipher with a 4 x 4
permutation matrix as the key. The obtained ciphertext is
THMA.
Find the matrix that was used as the key.

Algebra

Permutations and CombinationsProve that the triangles on the grid below are congruent by using the following methods:
1) SSS
2) SAS

Algebra

Permutations and CombinationsA population has the following characteristics.
(a) A total of 75% of the population survives the first year. Of that 75%, 25% survives the second year. The maximum life span is 3 years.
(b) The average number of offspring for each member of the population is 2 the first year, 4 the second year, and 2 the third year.
The population now consists of 176 members in each of the three age classes. How many members will there be in each age class in 1 year?

Algebra

Permutations and CombinationsSuppose you deposit your graduation cash gifts into an account that pays 4% annual interest compounded continuously. If you are 18 when you graduate, get $1000 in cash gifts and leave the money in the account until you are 30, how much money will you have? Round to the nearest dollar.

Algebra

Permutations and CombinationsConsider the following function and point.
F(x) = (x + 2)/(x-2)₁ (3,5)
(a) Find the derivative of the function.
f'(x) =
Find f'(x) when x = 3.
f'(3) =
Give the slope of the graph of the function at the given point (3, 5).
slope
Find an equation of the tangent line to the graph of f at the given point
y =

Algebra

Permutations and CombinationsHow many people must be chosen from 17
couples to be sure atleast one couple is
included?
a. 18
b. 17
c. 2
d. 3
e. 34

Algebra

Permutations and CombinationsFrom a deck of 52 cards, how many 5 cards tobe formed to be formed to have two pairs of
the same numbers example(two"l0s", and two"Qs or "2s" and two "S"s
a.109824
b.6864
C.247104
d.123552
e.27456

Algebra

Permutations and CombinationsConsider the following random sample of data:
2, -9, 3, -10, 5, -7, 9, 1, 4, 87
a) What is the mean of the sample data?
b) If the outlier is removed, what is the mean of the remaining sample data?

Algebra

Permutations and CombinationsIf light travels at a speed of 3 x 10⁸ m/s, and remembering the formula distance = speed x time. (or d = v*t), calculate the distance traveled by light in 2 milliseconds (i.e. in t = 2 x 10-³ seconds)

Algebra

Permutations and CombinationsWhat happens to the input when you plug it in?
Find expressions for the composite functions (MG) (t) and (Go M)(r). Explain in words what happens to your input when you plug it in to these composite functions. We call G and M inverses.

Algebra

Permutations and CombinationsGive the version of the Parallel Postulate as used in Euclidean geometry, beginning
the statement with, "Given a line and a point P not on,..."
Now show how to change this statement in two different ways, giving rise to two
different forms of non-Euclidean geometry.

Algebra

Permutations and CombinationsA chemist has three different acid solutions. The first acid solution contains 20 % acid, the second contains 40% and the third contains 60%. He wants to use all three solutions to obtain a mixture of 112 liters containing 35 % acid, using 3 times as much of the 60% solution as the 40 % solution. How many liters of each solution should be used?

Algebra

Permutations and CombinationsFind a basis for the orthogonal complement of the subspace of Rª spanned by the vectors.
V₁ = (1, 4, -4,3), V₂ = (3, 11, 3, 5), V3 = (1, 3, 11, -1)
The basis for the row space is
W₁ = (
W₂ = (
M.
i
"
i
i
1
1 0 )
0 1 )
.

Algebra

Permutations and CombinationsFind all solutions to sin (x + 4) + sin(x-4)=0 on [0, 2π).
Enter the answer in terms of , as needed. Do not enter a decimal approximation.

Algebra

Permutations and CombinationsTwo sides of a right triangle ABC (C is the
right angle) are given. Find the indicated
trigonometric function of the given angle.
Give exact answers with rational
denominators.
Find sin B when b = 5 and c = = 6.

Algebra

Permutations and CombinationsIf2-√3 is a root of a polynomial with integer coefficients, which of the following is another root?
2√3
3-√2
2+√3
√3-2

Algebra

Permutations and CombinationsA garden has width /13 and length 7/13. What is the perimeter of the garden in simplest radical form?
Select one:
O a. 16√13
O b. 91
O c. 8√13
Od. 14v13

Algebra

Permutations and Combinations2. Use the Law of Cosines to determine the
indicated angle O. (Assume a = 136.5, b = 59.2,
and c = 160.5. Round your answer to the nearest
degree.)
0 =

Algebra

Permutations and CombinationsExpress the proposition as an English sentence and determine whether it is true or false, where p and q are the propositions
p: "9.9=81" q: "8.10<7.11
The contrapositive of p →q
A. If 8.10 is not less than 7. 11, then 9.9 is not equal to 81; false
B. If 8.10 is not less than 7. 11, then 9.9 is equal to 81; false
C. If 8.10 is less than 7.11, then 9.9 is equal to 81; false
D. If 8.10 is less than 7.11, then 9.9 is not equal to 81; false

Algebra

Permutations and CombinationsWe distribute 30 indistinguishable toy cars to 3 people (say, A, B, and C). How distinguishable many ways can we do this so that no people get precisely 10 toy cars?

Algebra

Permutations and CombinationsDylan has 7 soccer trophies. He can only fit 4 trophies in a row on his display shelf. In how many different ways can Dylan arrange the trophies on the shelf?
Select on
O 28
O 840
O 35
O 210

Algebra

Permutations and CombinationsSamantha is arranging the letters in the word "MUSICAL." How many different 7-letter arrangements
can she make if she must use all seven letters each time?
Select one:
O 5040
O 7
O823,543
O28

Algebra

Permutations and Combinations(a) How many black playing cards must be drawn from a single deck of cards to be sure that at least two are the same suit?
(b) How many black playing cards must be drawn from a single deck of cards to be sure that at least twelve are spades or at least twelve are clubs?
(a) There must be at least _____ black playing cards drawn from a single deck of cards to ensure there are at least 2 of the same suit.
(b) There must be at least ________ black playing cards drawn from a single deck of cards to ensure there are at least twelve spades or twelve clubs.

Algebra

Permutations and CombinationsA hole is cut through the center of a thick sheet of metal. The metal is 8.5mm thick,10cm long and 13cm wide. The hole was 4cm wide. Find the weight of the metal. (in grams)

Algebra

Permutations and CombinationsFive thousand tickets are sold at $1 each for a charity raffle. Tickets are to bedrawn at random and monetary prizes awarded as follows: 1 prize of $500, 3 prizes of $200, 5 prizes of $30, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket?
Let X be the random variable for the amount won on a single raffle ticket.
E(X)=dollars (Round to the nearest cent as needed.)

Algebra

Permutations and CombinationsOn three rolls of a single die, you will lose $14 if a 3 turns up at least once, and you will win $8 otherwise. What is the expected value of the game?
Let X be the random variable for the amount won on a single play of this game.
E(X)= dollars (Type an integer or a decimal rounded to the nearest cent as needed.)

Algebra

Permutations and CombinationsWhich of the following situations can be modeled with a periodic function?
the height of a football after it has been thrown
the height of a person riding on an escalator
the height of a building after it has been constructed
the height of a pebble stuck in the tread of a tire