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
pav-90 [236]
3 years ago
15

A European high-speed passenger train is made up of two first-class passenger cars, five second-class cars, and a restaurant car

. How many ways can the train be made up?
Mathematics
1 answer:
Sliva [168]3 years ago
8 0

Answer:

The train can be made up in a total of \frac{8!}{5!2!} ways

Step-by-step explanation:

FIrst, lets assume that all cars are distinct. If that is the case, then, since we have a total of 8 cars, we have

- 8 possibilities for the first car

- 7 possibilities for the second car

- 6 possibilities for the third car

and so on.

So we have a total of 8! = 8*7*6*...*3*2*1 possibilities to make a train.

Now lets take into account that 5 of the cars are identical within each other. Then we could make a permutation of those 5 cars and we wouldnt notice. Hence, the order of the 5 cars of second-class doesnt matter and as a result, we should divide 8! by the total of possible permutations of the 5 second class cars, that it, 5!

We also need to divide the result by 2! = 2, because which first class car came first doesnt matter either. Therefore, the train can be made up in a total of \frac{8!}{5!2!} ways.

You might be interested in
A hiker climbed up from the bottom of a mountain. His elevation increased at a rate of 40 feet each hour. Which equation models
Nimfa-mama [501]

Answer:

I believe it is C

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Alexandria purchased a computer on sale. The original price was $1200. The sale price was 5/6 of the original price. how much di
Vaselesa [24]
I believe you ment to say sale price but I hope this helps you understand your question. The original price was 1200, and if it were 5/6 on sale (this method works for all questions like this) you would do 1200 ÷ 6 = 200 x 5 = $1000.
7 0
3 years ago
Michael cycled a distance of 12 5/6 miles in 2/3 hours. What is his cycling unit rate in miles per hour?
Annette [7]
19 1/2 miles per hour
4 0
3 years ago
Where will her cut be located? Round to the nearest tenth. x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 A
Arte-miy333 [17]

Answer:

The correct answer is 25.2 in.

Step-by-step explanation:

It is given that number line goes from 0 to 60 which can be used to represent a ribbon of length = 60 inches.

2 inches of the ribbon are frayed so actual length = 58 inches

Please refer to the attached image for the ribbon.

A is at 0

C is at 60

B is at 2

P is the point to divide the remaining ribbon in the ratio 2:3.

Part AB of the ribbon is frayed.

BP: PC = 2:3

Let BP = 2x and PC = 3x

Now, BP + PC = BC = 58 = 2x + 3x = 5x

So,

5x =58\\\Rightarrow x =11.6

BP = 2\times x = 2 \times 11.6 = 23.2\ inches

Location of the Cut = 2 + 23.2 = <em>25.2 inches</em>

<em></em>

Alternatively, we can use the formula directly:

x = \dfrac{m} {m + n } (x_2 - x_1) + x_1

x_1 = 2\\x_2 = 60

m: n is the ratio 2:3

x = \dfrac{2} {2 +3 } (60- 2) + 2\\\Rightarrow 0.4 (58 )+2\\\Rightarrow 23.2+2 \\\Rightarrow \bold{25.2\ inches}

5 0
3 years ago
Read 2 more answers
There is 1 inch of snow on the ground when it begins to snow 0.75 inch per hour. Which linear equation represents the total dept
aleksandrvk [35]
Y=0.75x+1 is the answer
3 0
3 years ago
Other questions:
  • Expression equivalent to 5(3m + n)
    15·1 answer
  • You are allowed to go to the store and spend your allowance on one of these three items: ball, candy, or hat. Which one would yo
    12·2 answers
  • The following group of values was entered into the TVM Solver of a graphing
    5·2 answers
  • (xy)^2 &lt;----this is the promblem......<br><br> WHAT IS THIS IN WORD FORM?
    10·1 answer
  • Why is 3 times 1/10 less than 3 times 10
    11·1 answer
  • Help I will give brainliest
    12·1 answer
  • Please guys I need help I don’t know how to do this
    8·1 answer
  • -63<br> —— = -7 what’s the error <br> -9
    5·2 answers
  • What is the area of the triangle 10,24,26
    6·1 answer
  • 4x – 8(2 - x) when x = 1/4?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!