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
lidiya [134]
3 years ago
12

In how many ways can 3 letters out of five distinct 5 distinct letters A, B, C, D and E be arranged in a straight line so that A

and B never come together?
Mathematics
1 answer:
anygoal [31]3 years ago
6 0

Answer:

5P3 - 18 =42 ways  

Step-by-step explanation:

For this case since the order matter we can use permutatiosn in order to solve the total number of ways on which we can order the 5 letters on this case we want to select 3 letters. We need to remember that the general formula for permutations is given by :

nPx = \frac{n!}{(n-x)!}

Where n is the total of letters and x the number of letters that we want to select.

For this case we have this for the total of possibilites:

5P3 = \frac{5!}{(5-3)!}= \frac{5*4*3*2!}{2!}=60 ways

But on this case we need another condition "A and B never come together". So for this case we can put on 6 ways 3 letters with A and B as we can see here:

X on this case represent any letter different from A or B (C,D or E)

AB X

AX B

X AB

BA X

B XA

X BA

Because the order matter on this case 6*3=18 are the total of ways that we can order this because we have 3 possible letters for X (C,D or E). And then the total of ways to select 3 letters where AB can't be together are:

5P3 - 18 =42 ways  

You might be interested in
Nate wants to visit his friend Mac before going to the park. Nates house is located at (-2,4) while the park is located at (10,2
defon

Answer:

(4, 3)

Step-by-step explanation:

If a point O(x, y) divides a line segment AB with end points at A(x_1,y_1) and      B(x_2,y_2) in the ratio of n:m, then the location of O is at:

x=\frac{n}{n+m} (x_2-x_1)+x_1\\\\y=\frac{n}{n+m} (y_2-y_1)+y_1

Given that Nates house is located at (-2,4) while the park is located at (10,2). Macs house if it is 1/2 of the distance from Nates house to the park (that is in the ratio of 1:1). Let (x, y) be the coordinate of Macs house, therefore:

x=\frac{1}{2}(10-(-2))+(-2)=\frac{1}{2}(12)-2=6-2\\\\x=  4\\\\y=\frac{1}{2}(2-4) +4=\frac{1}{2}(-2)+4\\\\y=3

The location of Macs house is (4, 3)

6 0
3 years ago
I know these are easy but I’m terrible at them someone help plz:))
Alex777 [14]

ummmmmmmmmmmmmm.................................. y would beeeeeeeeeeeeeeeeeee................................... ummmmmmmmmmmmmmmmmmmmmmmmmmmm.................... idk these confuse me. sorry.

5 0
3 years ago
Read 2 more answers
10.B. What number do you need to add/subtract/multiply/divide each side by in
Sindrei [870]

Step-by-step explanation:

step 1. m + 7.02 = 6.32

step 2. m = -0.70. (subtract 7.02 from each side)

5 0
3 years ago
What does it mean that there is an equal theoretical probability of each outcome ?
lara [203]

Answer:

there is equal probability for each outcome

Step-by-step explanation:

Let's say you are flipping a coin.

The possible outcomes are : Head and Tail

Probability(Head) = 1/2

Probability(Tail) = 1/2

In this case, there is equal theoretical probability of each outcome

5 0
2 years ago
Read 2 more answers
The airport has a moving walkway that moves at 2 feet per second. Suppose Calvin can travel 152
Rudiy27

Answer:

0.94 ft/sec

Step-by-step explanation:

Airport: 2 feet per second.

Total distance 152 ft in the same amount of time it takes him to talk 72 feet on the pavement.

152/2 = 76 - This is how many seconds he was walking in the airport.

He walked 76 seconds and moved 152 feet.

So that means if the SAME time was used so 76 seconds he walked 72 feet, then we can do 72ft/76sec to get 0.94ft/sec

5 0
3 years ago
Other questions:
  • Whitch is the equation of a line that is perpendicular to the lone represented by
    5·1 answer
  • If the length of FH is 18 units, what is the value if x
    15·1 answer
  • The formula v=r2h gives the volume of a cylinder with a radius r and height h. Find the volume of cylinder with radius (x+4) cm
    5·1 answer
  • I need the answer for 10 and how you got the answers
    6·1 answer
  • How do you convert meters per second to miles per hour?
    6·1 answer
  • There are only 7 days left until the launch of our new product and we only have 668.00 left in our promotion budget. We need to
    13·2 answers
  • PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU B
    15·1 answer
  • (Calculus)
    6·2 answers
  • Can you please solve​
    14·1 answer
  • On a piece of paper, graph y = - 2x - 3. Then determine which
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!