1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Shkiper50 [21]
3 years ago
12

Among the seven nominees for two vacancies on the city council are three men and four women. In how many ways may these vacancie

s be filled with any two of the nominees?
SAT
1 answer:
kodGreya [7K]3 years ago
6 0

Answer:

This question is incomplete

Complete Question

Among the seven nominees for two vacancies on the city council are three men and four women. In how many ways may these vacancies be filled

a) with any two of the nominees?

b) with any two of the women?

c) with one of the men and one of the women?

Answer:

a) 21 ways

b) 6 ways

c) 12 ways

Step-by-step explanation:

We solve this question using combination formula

C(n, r) = nCr = n!/r! (n - r)!

a) with any two of the nominees?

Probability (two of the nominees) = 7C2

= 7!/2! ×(7 - 2)!

= 7!/ 2! × 5!

= 7 × 6 × 5 × 4 × 3 × 2 × 1/2 × 1 ×(5 × 4 × 3 × 2 × 1)

= 21

b) with any two of the women?

We have a total of 4 women

Hence, the probability of any two of the four women, filling the vacancies =

P(any two of the women) = 4C2

= 4!/2! ×( 4 - 2)!

= 4!/ 2! × 2!

= 4 × 3 × 2 × 1/ 2 × 1 ×( 2 × 1)

= 6

c) with one of the men and one of the

Total number of men = 3

Total number of women = 4

= 3C1 × 4C1

= [3!/1! ×(3 - 1)! ] × [4!/1! ×(4 - 1)! ]

= [3!/1! × 2!] × [4!/1! ×3!]

= [3 × 2 × 1/ 1 × 2 × 1] × [4 × 3 × 2 × 1/ 1 × 3 × 2 × 1]

= 3 × [24/6]

= 3 × 4

= 12 ways

You might be interested in
Which factor influencing motivation would be most helpful to excel in sports?
CaHeK987 [17]

Answer:

a factor that will be helpful to excel is when they cheer it motivates you to try harder

Explanation:

3 0
3 years ago
Victor is concerned about his constant impulsive tendencies. He thinks something must be wrong with him. What is a healthy actio
zloy xaker [14]
Answer:

Listen to a mental health professional who can guide him through his troubles.

Taking medication without a doctors prescription isn’t really a healthy action
8 0
3 years ago
What did people place on the altars? a. a picture of the patron saint b. relics of the church’s patron saint c. triptychs of the
Anit [1.1K]
B) relics of the church’s patron saint
5 0
3 years ago
What are the moon phases
DIA [1.3K]

It's probably easiest to understand the moon cycle in this order: new moon and full moon, first quarter and third quarter, and the phases in between.

As shown in the above diagram, the new moon occurs when the moon is positioned between the earth and sun. The three objects are in approximate alignment (why "approximate" is explained below). The entire illuminated portion of the moon is on the back side of the moon, the half that we cannot see.

At a full moon, the earth, moon, and sun are in approximate alignment, just as the new moon, but the moon is on the opposite side of the earth, so the entire sunlit part of the moon is facing us. The shadowed portion is entirely hidden from view.

The first quarter and third quarter moons (both often called a "half moon"), happen when the moon is at a 90 degree angle with respect to the earth and sun. So we are seeing exactly half of the moon illuminated and half in shadow.

Once you understand those four key moon phases, the phases between should be fairly easy to visualize, as the illuminated portion gradually transitions between them.

An easy way to remember and understand those "between" lunar phase names is by breaking out and defining 4 words: crescent, gibbous, waxing, and waning. The word crescent refers to the phases where the moon is less than half illuminated. The word gibbous refers to phases where the moon is more than half illuminated. Waxing essentially means "growing" or expanding in illumination, and waning means "shrinking" or decreasing in illumination.

Thus you can simply combine the two words to create the phase name, as follows:

After the new moon, the sunlit portion is increasing, but less than half, so it is waxing crescent. After the first quarter, the sunlit portion is still increasing, but now it is more than half, so it is waxing gibbous. After the full moon (maximum illumination), the light continually decreases. So the waning gibbous phase occurs next. Following the third quarter is the waning crescent, which wanes until the light is completely gone -- a new moon.


5 0
3 years ago
Read 2 more answers
In the system of equations above, k is a constant and x and y are variables.for what value of k will the system of equations hav
ivann1987 [24]

......................................

6 0
3 years ago
Other questions:
  • Is it possible to get banned on brainly.com?
    5·1 answer
  • One type of potential energy is elastic energy. This is energy stored up and then released by objects that can stretch and snap
    6·1 answer
  • Which uses electromagnetic radiation to discover the properties and composition of bodies in space?
    8·2 answers
  • What is the smallest positive number that can be created with four decimal places using the numbers 1, 2, 4, and 8?
    6·2 answers
  • P(A|B) represents the probability that
    15·2 answers
  • What can you tell about Jim from these paragraphs? Include information from the story in your answer.
    7·1 answer
  •  What have you learned from the movie(gospel of john) that you want to include to your personal life?
    7·1 answer
  • Approximately 80% of all job openings are part of the hidden job market. Please select the best answer from the choices provided
    14·1 answer
  • The writer is working on a revision of the passage and has written the following thesis statement for it. Based on the evidence
    11·1 answer
  • Explain the historical circumstances that led to british attitudes about their empire as shown in this excerpt from an abc for b
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!