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
Rainbow [258]
3 years ago
13

A company must select 4 candidates to interview from a list of 12, which consist of 8 men and 4 women.

Mathematics
2 answers:
Snowcat [4.5K]3 years ago
8 0
<span>Selections of 4 candidates regardless of gender would result in 12c4, or 12!/(8!*4!) = 9*10*11*12 = 495 possibilities. Selections of 4 candidates where exactly two must be women would result in 8c2 (for the men) * 4c2 (for the women) = 8!/(6!*2!) * 4!/(2!*2!) = 28 * 6 = 168 possibilities. Selections of 4 candidates where AT LEAST two must be women would result in the above 168 (2 women) plus groups where there are exactly three women (8c1*4c3 = 8*(4!/(3!*1!) = 8*4 = 32) plus groups where there are exactly 4 women (1). So there are 168 + 32 + 1 = 201 possible selections of 4 from this group where at least 2 are women.</span>
Radda [10]3 years ago
7 0
Part A

If 4 candidates were to be selected regardless of gender, that means that 4 candidates is to be selected from 12.

The number of possible selections of 4 candidates from 12 is given by

^{12}C_4= \frac{12!}{4!(12-4)!}= \frac{12!}{4!\times8!} =11\times5\times9=495

Therefore, the number of <span>selections of 4 candidates regardless of gender is 495.



Part B:

</span>
<span>If 4 candidates were to be selected such that 2 women must be selected, that means that 2 men candidates is to be selected from 8 and 2 women candidates is to be selected from 4.

The number of possible selections of </span><span>2 men candidates from 8 and 2 women candidates from 4 is given by

</span><span>^{8}C_2\times ^{4}C_2= \frac{8!}{2!(8-2)!}\times &#10;\frac{4!}{2!(4-2)!} \\  \\ = &#10;\frac{8!}{2!\times6!}\times\frac{4!}{2!\times2!} &#10;=4\times7\times2\times3=168

Therefore, the number of selections of 4 candidates </span><span>such that 2 women must be selected is 168.</span>



Part 3:

If 4 candidates were to be selected such that at least 2 women must be selected, that means that 2 men candidates is to be selected from 8 and 2 women candidates is to be selected from 4 or 1 man candidates is to be selected from 8 and 3 women candidates is to be selected from 4 of <span>no man candidates is to be selected from 8 and 4 women candidates is to be selected from 4.

The number of possible selections of </span>2 men candidates from 8 and 2 women candidates from 4 of <span>1 man candidates from 8 and 3 women candidates from 4 of no man candidates from 8 and 4 women candidates from 4 is given by
</span><span>
^{8}C_2\times ^{4}C_2+ ^{8}C_1\times ^{4}C_3+ ^{8}C_0\times ^{4}C_4 \\  \\ = \frac{8!}{2!(8-2)!}\times \frac{4!}{2!(4-2)!}+\frac{8!}{1!(8-1)!}\times \frac{4!}{3!(4-3)!}+\frac{8!}{0!(8-0)!}\times \frac{4!}{4!(4-4)!} \\ \\ = \frac{8!}{2!\times6!}\times\frac{4!}{2!\times2!}+\frac{8!}{1!\times7!}\times\frac{4!}{3!\times1!}+\frac{8!}{0!\times8!}\times\frac{4!}{4!\times0!} \\  \\  =4\times7\times2\times3+8\times4+1\times1=168+32+1=201

Therefore, the number of selections of 4 candidates </span><span>such that at least 2 women must be selected is 201.</span>

You might be interested in
Please answer Fast!!!! I will award 100 points for correct answer
Tasya [4]

Answer:

52

Step-by-step explanation:

56+(x+72) =180

180 because it is supplementary

8 0
2 years ago
Read 2 more answers
Give an example of when and why one would use a continuity correction factor?
iris [78.8K]

Answer:

An example of when a continuity correction factor can be used is in finding the number of tails in 50 tosses of a coin within a given range .

and continuity correction factor is used when a continuous probability distribution is used on a discrete probability distribution

Step-by-step explanation:

An example of when a continuity correction factor can be used is in finding the number of tails in 50 tosses of a coin within a given range .

continuity correction factor is used when a continuous probability distribution is used on a discrete probability distribution,  continuity correction factor creates an adjustment on a discrete distribution while using a continuous distribution

3 0
3 years ago
What the simplest form for 5 4/32?
stira [4]
Ok so the answer is 160/32
4 0
2 years ago
Read 2 more answers
A triangle has angles in the ratio 3:10:2 what is the size of the largest angle x?
Annette [7]

Answer:

B

Step-by-step explanation:

let the angles be 3k,10k,2k

then 3k+10k+2k=180

15k=180

k=180/15=12

x=10k=10×12=120°

5 0
3 years ago
I need help fast I appreciate it fam
Vanyuwa [196]

I think the answer is 12.9

5 0
2 years ago
Other questions:
  • I need the answer pls help!
    12·1 answer
  • Sarah and her family just got back from vacation they had been travelling for 3 days driving 8 1/2 hours each day how many hours
    12·1 answer
  • Alina has just recieved 3 video games for her birthday to add to her existing 12 video games. A week later she went to the thrif
    5·1 answer
  • The sum of 185 and h as an algebraic expressions
    9·2 answers
  • Solve the system of equations.<br>y= 2x + 4<br>y = x2 + x - 2​
    14·1 answer
  • There was a blizzard. Snow was falling at a rate of 4 ½ inches per hour. If the snow kept accumulating at the same rate, how lon
    6·1 answer
  • I’m confused on this one
    9·1 answer
  • What is the square root of pi
    9·2 answers
  • (2x + 3)^2 - 4(2x + 3) = 0
    5·1 answer
  • Please help!!!! Circle U is shown. Chords R T and Q S intersect at a point forming 4 angles. The top left angle is angle 1, and
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!