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
Juli2301 [7.4K]
3 years ago
5

A committee consists of eight women and twelve men. Three committee members will be chosen as officers. What is the probability

that all the officers are women?
Social Studies
2 answers:
FromTheMoon [43]3 years ago
7 0

Answer:

0.049 (approximately)

Explanation:

Solution:

Since there is 8 women and 12 men, from which 3 are chosen as officers.

Use C(n,r)=n! ÷ (r!(n-r)!) to represent number of combinations of taking r objects out of n.

Therefore;

Ways to choose 3 women out of 8 = C(8, 3)

Ways to choose from 20 members = C(20,3)

Probability of choosing 3 women out of 20

= C(8,3)÷ C(20,3)

Substituting our values for n=8 and r=3 we get

8! ÷ 3!(8-3)!

Substituting 8-3 with 5

8! / 3!×5!

Expanding factorial and cancelling out

8×7×6×5! ÷ 3!×5!

Multiple out

336÷6 = 56

Substituting our values for n=8 and k=3 we get

20! ÷ 3!(20-3)!

Substituting 20-3 with 17

20! ÷ 3!×17!

Expanding factorial and cancelling out

20x19x18x17! ÷ 3!×17!

Multiple out

6840÷6

= 1140

= 56/1140

= 3/17

=0.049 (approximately)

MariettaO [177]3 years ago
6 0

Answer:

The probability that all the officers are women is \frac{56}{1140}

Explanation:

Given a committee consisting of 8 women and 12 men, from which 3 committee members are to be chosen as officers from a committee.  

The total number of committee members is 8 + 12 = 20 members

C(n,r) = \frac{n!}{r!(n-r)!} which represents the number of combinations of taking r objects out of n.

The probability that all the officers are women = C(8,3) / C(20,3)

= \frac{8!}{3!(8-3)!} / \frac{20!}{3!(20-3)!}

=\frac{8!}{3!5!} /\frac{20!}{3!17!}

=\frac{56}{1140}

Therefore the probability that all the officers are women is \frac{56}{1140}

You might be interested in
Global warming has been in the foreground of politics and science for quite some time. There have been numerous studies conducte
Lunna [17]

The correct answer to this open question is the following.

Although there are no options attached we can say the following.

Indeed, global warming has been in the foreground of politics and science for quite some time. There have been numerous studies conducted on the effects of global warming and what we might do to mitigate any threats. I think some policymakers are wary of the findings and some can trust that the conclusions are sound for the following reason.

Politicians are wary because, in reality, there are no 100% conclusive arguments that confirm that global warming is the result of humans. For other politicians, the evidence provided by environmental institutions is valid and they are prompt to proclaim that humans are to blame for global warming.

What is real, is that earth scientists think that global warming caused significant climate change in the past. And when they say the past, they mean a time before humans appeared on planet earth.

Climate change or global warming is not new for planet earth. It is a phenomenon that has happened in the past according to scientists and national agencies. It is believed that global warming had caused natural disasters such as the melting of ice caps and the flooding of many lands on Earth, destroying life forms.

That is why right now, many agencies are closely researching climate change. Among those institutions are the US National Academy of Sciences, the Geological Society of America, the American Meteorological Society, and the National Aeronautics and Space Administration.

3 0
3 years ago
What does "separation of powers" mean? (3 points)
Salsk061 [2.6K]

Answer:

A.

Explanation:

5 0
3 years ago
Mention the needs of development.​
natita [175]
Ans: The basic needs approach to development was endorsed by governments and workers' and employers' organizations from all over the world. Many modern lists emphasize the minimum level of consumption of 'basic needs' of not just food, water, clothing and shelter, but also sanitation, education, and healthcare.
4 0
2 years ago
Which of the following statements is true? a.Online instruction has been found to be effective for all learners. b.Online instru
Minchanka [31]
<h3>d.Classroom instruction is more effective than online instruction for teaching declarative knowledge.</h3>

Explanation:

Though online instruction have been proved as a reliable source of learning, there are some learning processes which may have better results if taught in the classrooms.

One such case is imparting declarative knowledge. Declarative Knowledge is essentially descriptive and conceptual information which describes a certain topic in a detailed manner.

It requires a lot of time and effort to impart declarative knowledge. Therefore, classroom instruction proves more effective than online instruction while imparting declarative knowledge.

6 0
3 years ago
When drivers and motorcyclists share the road with pedestrians, whose responsibility is it to do everything possible to avoid a
asambeis [7]
I believe <span>the driver.</span>
5 0
3 years ago
Read 2 more answers
Other questions:
  • What are the types of borders?
    15·2 answers
  • Trina and Uri do business as Value Gems. In acting on the firm's behalf in a deal with World Diamond Exchange, Trina recklessly
    10·2 answers
  • Which of the following is a main economic variable that affects business cycles?
    11·1 answer
  • Which statement accurately describes the ways culture changes?<br> Group of answer choices
    6·1 answer
  • Worldwide men and women are only permitted to have monogamous marriages. Please select the best answer from the choices provided
    6·2 answers
  • In which region of the global south are women's literacy rates closer to those of men?
    13·1 answer
  • Why did Georgia have to write a new state constitution?
    6·2 answers
  • What is the answer to this?
    6·2 answers
  • So if humans first evolved in africa how do you think they ended up in the americas?
    8·1 answer
  • Fay is mentally incompetent but has not been so adjudged by a court. any contract fay enters into is:_________
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!