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
zavuch27 [327]
2 years ago
8

7) PG & E have 12 linemen working Tuesdays in Placer County. They work in groups of 8. How many

Mathematics
1 answer:
BabaBlast [244]2 years ago
5 0

Part A

Since order matters, we use the nPr permutation formula

We use n = 12 and r = 8

_{n}P_{r} = \frac{n!}{(n-r)!}\\\\_{12}P_{8} = \frac{12!}{(12-8)!}\\\\_{12}P_{8} = \frac{12!}{4!}\\\\_{12}P_{8} = \frac{12*11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1}\\\\_{12}P_{8} = \frac{479,001,600}{24}\\\\_{12}P_{8} = 19,958,400\\\\

There are a little under 20 million different permutations.

<h3>Answer: 19,958,400</h3>

Side note: your teacher may not want you to type in the commas

============================================================

Part B

In this case, order doesn't matter. We could use the nCr combination formula like so.

_{n}C_{r} = \frac{n!}{r!(n-r)!}\\\\_{12}C_{8} = \frac{12!}{8!(12-8)!}\\\\_{12}C_{8} = \frac{12!}{4!}\\\\_{12}C_{8} = \frac{12*11*10*9*8!}{8!*4!}\\\\_{12}C_{8} = \frac{12*11*10*9}{4!} \ \text{ ... pair of 8! terms cancel}\\\\_{12}C_{8} = \frac{12*11*10*9}{4*3*2*1}\\\\_{12}C_{8} = \frac{11880}{24}\\\\_{12}C_{8} = 495\\\\

We have a much smaller number compared to last time because order isn't important. Consider a group of 3 people {A,B,C} and this group is identical to {C,B,A}. This idea applies to groups of any number.

-----------------

Another way we can compute the answer is to use the result from part A.

Recall that:

nCr = (nPr)/(r!)

If we know the permutation value, we simply divide by r! to get the combination value. In this case, we divide by r! = 8! = 8*7*6*5*4*3*2*1 = 40,320

So,

_{n}C_{r} = \frac{_{n}P_{r}}{r!}\\\\_{12}C_{8} = \frac{_{12}P_{8}}{8!}\\\\_{12}C_{8} = \frac{19,958,400}{40,320}\\\\_{12}C_{8} = 495\\\\

Not only is this shortcut fairly handy, but it's also interesting to see how the concepts of combinations and permutations connect to one another.

-----------------

<h3>Answer: 495</h3>
You might be interested in
If 8 = x + y and y &gt; 0, then x is ___ 8.
qaws [65]
The answer is B because if 0 is < y than 8 would be equal to x

5 0
3 years ago
Do not use spaces in your answer. Solve for x. -5x + 12x - 8x = -24 x = ___ a0
const2013 [10]

Answer:

\Huge \boxed{x=24}

Step-by-step explanation:

-5x + 12x - 8x = -24

Combine all like terms.

(-5+ 12- 8)x = -24

-x=-24

Multiply both sides by -1.

x=24

7 0
3 years ago
Read 2 more answers
Each of the following tables defines a relationship between an input x and an output y. Which of the relationship respresent fun
sveticcg [70]

Answer:

wat

Step-by-step explanation:

nose

6 0
3 years ago
SOMEONE PLEASE ANSWER ASAP THIS FOR BRAINLIEST!!!!
kirill115 [55]

wow the answer is not listed on option

3 0
3 years ago
Through: (6, 2), perpendicular to<br> y = -x-5 <br> in slope intercept form
True [87]

Answer:

y = x-4

Step-by-step explanation:

y = -x-5

Slope of line is -1.

Slope of perpendicular to line is 1.

Point-slope equation for line of slope 1 that passes through (6,2):

y-2 = 1(x-6)

Rearrange equation to slope-intercept form:

y = 1(x-6) + 2

y = x-4

6 0
3 years ago
Other questions:
  • "A movie data base claims that the average length of movies is 117 minutes. A researcher collected a random sample of 160 movies
    5·1 answer
  • The graph below shows a dilation. Jacky says that the original image was enlarged, but Juan thinks the original image was reduce
    9·1 answer
  • What is the theoretical probability of the spinner landing on Elisondra’s section?
    10·1 answer
  • Find the distance between (-8, -1) and (0, 5). Give your answer in simplest radical form.
    12·1 answer
  • Is this right?<br> plz tell me
    6·2 answers
  • What is the solution of the equation?
    5·2 answers
  • The soccer team has to order new uniforms. Their shorts cost $10, the jersey costs $15, and their socks cost $18. If there are 2
    15·2 answers
  • In the phrase rise over run<br> what does rise indicate
    5·2 answers
  • Solve for x -5(x-4)=-30
    14·1 answer
  • How do the values of the 5s in 581.03 and 5.472 compare
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!