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
Contact [7]
3 years ago
11

Consider strings of length 10 which contain only letters from the set {A, E, I, O, U} and digits from {1, 3, 5, 7, 9}. Suppose r

epitition of letters is not allowed.
How many different strings are there?
How many different strings are there if the letters, i.e. A, E, I, O, U and the digits, i.e. 1,3, 5, 7, 9 must alternate?
How many different strings are there if all five letters must be adjacent in each string?
Mathematics
1 answer:
Akimi4 [234]3 years ago
5 0

Answer:

a) There are 3,628,800 different strings.

b) There are 28,800 different strings if the letters ad digits must alternate.

c)There are 86,400 different string if all five letters must be adjacent in each string.

Step-by-step explanation:

There are 10 digits.

Our strings have the following format:

C1 - C2 - C3 - C4 - C5 - C6 - C7 - C8 - C9 - C10

repitition of letters is not allowed.

a) How many different strings are there?

C1 can be any of the 10, C2 can be 9, C3 can be 8, ...

So in total there are:

T = 10*9*8*7*6*5*4*3*2*1 = 3,628,800

There are 3,628,800 different strings.

b) How many different strings are there if the letters, i.e. A, E, I, O, U and the digits, i.e. 1,3, 5, 7, 9 must alternate?

There are the following possiblities:

5(l) - 5(d) - 4(l) - (4d) - ...

Or

5(d) - 5(l) - 4(d) - 4(l) - ...

So:

T = 2*(5*5*4*4*3*3*2*2*1*1) = 28,800

There are 28,800 different strings if the letters ad digits must alternate.

c) How many different strings are there if all five letters must be adjacent in each string?

L - L - L - L - L - D - D - D - D - D

D - L - L - L - L - L - D - D - D - D

D - D - L - L - L - L - L - D - D - D

D - D - D - L - L - L - L - L - D - D

D - D - D - D - L - L - L - L - L - D

D - D - D - D - D - L - L - L - L - L

There are T = 6*(5*5*4*4*3*3*2*2*1*1) = 86,400

There are 86,400 different string if all five letters must be adjacent in each string.

You might be interested in
PLEASE HELP WITH THESE 4 questions I DONT GET IT ASAP thank you in advance
alex41 [277]

Answer:

2. 31/6  3. -12/1   4. integer  5. rational number

Step-by-step explanation:

2. You multiply the 5 by 6/6, so it becomes 30/6, then add the 1/6. getting you the 31/6.

3. Since -12 is already an integer with no mixed part, you just put it over 1.

4. -12 is an integer, but is not a whole number because it is negative.

5. fractions are rational numbers

4 0
3 years ago
Read 2 more answers
Please answer 1-7 I BEG YOU I WILL MARK BRAINLIEST
enot [183]
Use the Circumference Formula of a Circle: C=2(pi)(r). The radius is the length from the center to a point on the circle. The circumference is essentially the perimeter of the circle, so the “edge” around the circle is the circumference.
8 0
2 years ago
Read 2 more answers
I need help with these questions, thanks!
kifflom [539]

Answer:

????

Step-by-step explanation:

number 1 could be 2 different answers

7 0
3 years ago
The scatter plot above show the relationship between the number of bags of popcorn that are sold and the price per bag. Which is
saul85 [17]
The independent variable is is the price per bag.
4 0
3 years ago
Triangle ABC has vertices at A(1,2) B(4,6) and C(4,6) in the coordinate plane. The triangle will be reflected over the x-axis an
k0ka [10]
You should know that you can predict changes in coordinates after translations without a graph or anything like that.

(x, y) reflected over the x axis = (x, -y)
(x, y) reflected over the y axis = (-x, y)
(x, y) rotated 90 degrees around the origin = (y, -x)
(x, y) rotated 180 degrees around the origin = (-x, -y)
(x, y) rotated 270 degrees around the origin - (-x, y)

So here's our set of points.
A(1, 2), B(4, 6), C(4, 6)

Here's those points reflected over the x axis.
A'(1, -2), B'(4, -6), C'(4, -6)

And here's <em>those</em> points rotated 180° around the origin.
A''(2, -1), B''(6, -4), C''(6, -4)

I think you made a mistake writing down the question, though, because B and C are the same yet you say ABC forms a triangle. You should be able to go through this process with whatever the coordinate was supposed to be.
4 0
2 years ago
Other questions:
  • Currently, there are 420 cars in the parking lot. Campus security needs the set up for an event. They have only ten minutes to m
    13·1 answer
  • Find the median of the data set: 9, 6, 7, 3, 10, 9<br><br> ASAP PLEASE
    12·2 answers
  • Simplify the following expression: (9x^2+2x−5)+(6x^2−5x+4). Please explain how you found your answer
    11·1 answer
  • I don't understand what to write
    12·1 answer
  • Which of the following angles is coterminal with -4pi/3?<br><br> -2pi/3<br> -pi/3<br> pi/3<br> 2pi/3
    12·1 answer
  • Ms.Jonhson and Ms.Siple were folding report cards to send home to parents. The ratio of number of report cards Ms.Jonhson folded
    12·1 answer
  • Area of a trapezoid: 9 m by 15m by 20m
    6·2 answers
  • Please understand the explanation
    9·1 answer
  • Please help ill mark brainliest!
    14·1 answer
  • imagine that you write each letter of the word california on individual cards. you shuffle them, turn them facedown on a table,
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!