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
Help pls :’( ASAPP!!!<br> “Complete the proof”
nata0808 [166]

1) \overline{AB} \cong \overline{CD}, \overline{AD} \cong \overline{CB}, \overline{AX} \perp \overline{BD}, \overline{CY} \perp\overline{BD} (given)

2) \overline{BD} \cong \overline{BD} (reflexive property)

3) \triangle ABD \cong \triangle ACDB (SSS)

4) \angle ADB \cong \angle CBY (CPCTC)

5) \angle CYB and \angle AXD are right angles (perpendicular lines form right angles)

6) \triangle CYB and \triangle AXD are right triangles (a triangle with a right angle is a right triangle)

7) \triangle AXD \cong \triangle CYB (HA)

8) \overline{AX} \cong \overline{CY} (CPCTC)

6 0
2 years ago
What is the value of p
Elan Coil [88]

Answer:

B. 40

Step-by-step explanation:

p is the opposite of 140.

180 - 140 = 40

6 0
3 years ago
Read 2 more answers
What is the shape of the horizontal cross section of the
GuDViN [60]

Answer: Pentagon

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Alice earned some money over the summer. She charged $11 per hour to baby-sit and $7.50 per hour to mow lawns. She baby-sat for
Ronch [10]
(11 * 25) + (7.5 * 19) = 

$417.50 
5 0
3 years ago
Read 2 more answers
Which of the following expressions represents the solution to x – 3 &gt; -4?
Bess [88]

Step-by-step explanation:

x - 3 > -4

= x > -4+3

= x > -1 _ Answer

8 0
3 years ago
Other questions:
  • Select all of the coefficients in the expression. 12xy3 + 2x5y + 4x5y2 + 7x5y.
    5·1 answer
  • A square hamburger is centered on a circular bun. Both the bun and the burger have an area of 16 square inces. How far to the ne
    12·1 answer
  • True or false:opposite angles of a rhombus are supplementary
    10·1 answer
  • Please need help with one. I did it the first time and I know it’s not B
    11·1 answer
  • I can't figure this out
    9·2 answers
  • Type in the missing terms in this sequence of square numbers.
    6·1 answer
  • Jennifer uses a coupon for 20% off her order. is the total was 18$ how much money does she save
    7·2 answers
  • January 19 national popcorn day. A bag of popcorn has the average of 450 kennels if 4%% of the kernels dont pop how manu pieces
    12·1 answer
  • Adwoa received a commission of 20% on a bread she sold. in one week, Adwoa's commission was Gh¢540.00.
    7·1 answer
  • help quick pls At a company, copy machine prints 175 pages in 5 minutes. If the number of pages printed is proportional to the t
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!