Question

Evaluate C(11,4). C(11,4) equals =

Six cards are marked with the numbers 1, 2, 3, 4, 5, and 6 , then shuffled, and three cards are drawn.

a. How many different three -card combinations are possible?

b. How many three -card hands contain a number less than three?

Use a tree diagram for the following. a. Find the number of ways 2 letters can be chosen from the set {U, V, W, X} if order is important and repetition is allowed.

b. Reconsider part a if no repeats are allowed.

c. Find the number of combinations of 4 elements taken 2 at a time. Does this answer differ from part a or b?

How many different committees can be formed from 8 teachers and 33 students if the committee consists of 2 teachers and 4 students? In how many ways can the committee of 6 members be selected?__

In a game of musical chairs, 5 children will sit in 4 chairs arranged in a row (one will be left out). In how many ways can this happen, if we count rearrangements of the children in the chairs as different outcomes? Is this problem a permutation or a combination?

Marbles are being drawn without replacement from a bag containing 10 marbles. First, decide whether this situation involves permutations or combinations. Then, in the following cases, determine the possible number of samples that can be drawn. Does this problem use combinations or permutations?

An urn contains 7 white balls and 9 red balls. Three balls are selected. In how many ways can the 3 balls be drawn from the total of 16 balls: (a) If 2 balls are white and 1 is red? (b) If all 3 balls are white? (c) If all 3 balls are red?

From a group of 8 newly hired office assistants, 3 are selected. Each of these 3 assistants will be assigned to a different manager. In how many ways can they be selected and assigned? The office assistants can be selected and assigned in __ different ways.

A group of 22 workers decides to send a delegation of 6 to their supervisor to discuss their work assignments. In the following cases, determine the possible number of delegations. The number of possible 6 -person delegations is __ .

A company sells regular hamburgers as well as a larger burger. Either type can include cheese, relish, lettuce, tomato, mustard, or ketchup. a. How many different hamburgers can be ordered with exactly 3 extras? b. How many different regular hamburgers can be made that use any 3 of the extras? c. How many different regular hamburgers can be ordered with at least 2 extras?

Jeanine Baker makes floral arrangements. She has 14 different cut flowers and plans to use 6 of them. How many different selections of the 6 flowers are possible? How many ways can the 6 flowers be chosen?

Answer #1

A “superfecta” is correctly guessing the top four horses in
order in a horse race.
(a) If there are 8 horses in a race, how many different
superfectas are possible?
(b) “Boxing” a superfecta means that you get to choose the four
horses for the superfecta without regard to order. How many box
superfectas are possible?
(c) If a bet on a superfecta costs 10 cents. How much would you
expect for a box superfecta to cost? (Hint: Think about...

Two balls are drawn without replacement from an urn with 5 red,
3 white, 6 blue balls. Find the number of ways for selecting two
balls:
a). with the same
color
b). with different colors
c). 1 red, 1
white
d). red or white

ind the number of ways of selecting 12 balls from 6 red bal
COMBINATION
Solve each of the following problems. (Show your work.)
Find the number of ways of selecting 12 balls from 6 red balls,
5 white balls and 5 blue balls if each selection consists of 4
balls of each color.
Among the seven nominees for two vacancies on the city council
are four men and six
women. In how many ways may these vacancies be filled...

1.A bag contains 5blue, 4 red, and 3green marbles. Four
marbles are drawn at random from the bag. How many different
samples are possible which include exactly two red marbles?
2.A bag contains 5 blue, 3 red, and 4 green marbles. Four
marbles are drawn at random from the bag. How many different
samples are possible which include at least one marble of each
color

Circular Permutations and Permutations with Similar Elements
1) In how many ways can three people be made to sit at a round
table?
2) In how many ways can three couples be seated at a round
table, so that men and women sit alternately?
3) In how many ways can five keys be put on a key ring?
4) Find the number of different permutations of the letters of
the word MATHEMATICS.
5) How many different ways can three pennies,...

The staff at a small company includes: 4 secretaries, 20
technicians, 4 engineers, 2 executives, and 50 factory workers. If
two people are selected at random for a task, what is the
probability that they will be an engineer and an executive?
A =4/80*2/79+2/80*4/79 or
=COMBIN(4,1)*COMBIN(2,1)*COMBIN(74,0)/COMBIN(80,2)
B =4/80*2/79
C =4/80*2/80
D = COMBIN(4,2)*COMBIN(2,2)*COMBIN(74,0)/COMBIN(80,2)
How many ways could people rank the top three cows from a herd
of ten.
A 120
B 720
C 210
D 5,040
On a snack tray...

A) How many permutations of 7 objects, taking 3 at a time?
Group of answer choices: 210, 35, 5040, 6
B) How many ways can 4 books be arranged on a shelf, if they can
be selected from 12 books?
C) How many ways can a committee of 4 people be selected from a
group of 8 people?
D) If the letters A, B, C, D, E, and F are to be used in a
five-letter code, how many different...

Please answer the
following combinatorics questions. Please write your answers as
whole numbers (e.g., "4").
How many ways can you order 7 people?
I have 12 different soccer balls, but I'm only going to take 2
of them to the game. How many different sets of 2 are possible
where order does not matter?
A professor has a test bank with 8 different questions in it,
for a particular group of questions on her test, she will only ask
3...

All six different robots have to be assigned to three different
tasks. Three (3) robots have wheels only (Type I) and the other
three (3) having legs only (Type II). Individual performance of the
robots varies for a pending task due to the differences in failure
rates, reliability and adaptability. Answer the following
questions
: 1) If we plan to assign one (1) robot to Task 1, two (2)
robots to Task 2, and three (3) to Task 3, in...

1. An experiment consists of drawing balls from an urn which
contains 2 red balls, one white ball, and one
blue ball. The balls are drawn, without replacement, until
either a blue ball has been drawn or two different
colors have been drawn. If an outcome of this experiment
consists of an ordered list of the colors of the
balls drawn, how may outcomes exist?
2. An experiment consists of repeatedly drawing a ball from an
urn which contains 3...

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