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
melamori03 [73]
3 years ago
14

In another state, all license plates consist of from four to six symbols chosen from the 26 letters of the alphabet together wit

h the ten digits 0–9.
a. how many license plates are possible if repetition of symbols is allowed?
b. how many license plates do not contain any repeated symbol? h
c. how many license plates have at least one repeated symbol?
d. what is the probability that a license plate chosen at random has a repeated symbol?
Mathematics
1 answer:
fredd [130]3 years ago
3 0
A)
First note that the plates can have between 4 and 6 symbols so we will need to find the number of plates with 4 symbols, 5 symbols and 6 symbols. We add these to get the total. In this part repetition of symbols is allowed. Since there are 26 + 10 =36 possible symbols we look at each position on the plate and think of how many choices there are. We multiply the number f choices using the counting principal since the choices are each independent -- one symbol does not affect another. There are 36 choices for the first symbol, 35 for the second and so on. The number of plates is:
4-symbols = (36)(36)(36)(36)=36^4
5 symbols = (36)^5
6 symbols = 36^6
So the total here is: 36^4+36^5+36^6

B) Here we do not repeat symbols so there are 36 choices for the first symbol but only 35 for the next and 34 for the one after and so on.
4-symbols = (36)(35)(34)(33)
5 symbols = (36)(35)(34)(33)(32)
6 symbols = (36)(35)(34)(33)(32)(31)
So the total here is: (36)(35)(34)(33)+(36)(35)(34)(33)(32)+(36)(35)(34)(33)(32)(31)

c)
In order for there to be a repeated symbol we have 36 choices for the first symbol, 36 for the next and so on. However, for the last symbol we have to pick from one of the ones already selected so there are 3, 4 or 5 choices respectively.
4-symbols = (36)(36)(36)(3)
5 symbols = (36)(36)(36)(36)(4)
6 symbols = (36)(36)(36)(36)(36)(5)
So the total here is: (36^3)(3)+(36^4)(4)+(36^5)(5)

D)
The probability is given by (the number of plates with at least one repeated symbol)/(the total number of plates if repetitions are allowed) = (the answer to c) / (the answer to a)
You might be interested in
Why does the square root of 64 have a positive and negative value?
barxatty [35]
Because it means it has two answers when -8×-8 it equals 64 so is 8×8
in math when negative multiply negative it will be positive...
5 0
3 years ago
If the expression above is rewritten in the form a+bi, where a and b are real numbers, what is the value of a? ​
Harman [31]

Answer:

......................................,........

8 0
3 years ago
In the expression , 5.28 x 10^3 , which number is the base ?
solong [7]
Bse is 10
x^m, x is base of exponent
7 0
3 years ago
Let Upper A equals left bracket Start 2 By 2 Matrix 1st Row 1st Column negative 2 2nd Column 4 2nd Row 1st Column 1 2nd Column 3
vagabundo [1.1K]

Answer:

not

Step-by-step explanation:

\left[\begin{array}{ccc}-2&4\\1&3\end{array}\right] *\left[\begin{array}{ccc}-2&1\\3&7\end{array}\right]=

First is A and Second is B

Let's find A*B

\left[\begin{array}{ccc}-2(-2)+4*3&-2*1+4*7\\1(-2)+3*3&1*1+3*7\end{array}\right] =\left[\begin{array}{ccc}16&26\\7&22\end{array}\right]

b)

\left[\begin{array}{ccc}-2&1\\3&7\end{array}\right]  \left[\begin{array}{ccc}-2&4\\1&3\end{array}\right] =

Now let's find B*A

\left[\begin{array}{ccc}-2(-2)+1*1&-2*4+1*3\\3(-2)+7*1&3*4+7*3\end{array}\right] =\left[\begin{array}{ccc}5&-5\\1&23\end{array}\right]

c) They are not

7 0
2 years ago
A multivitamin tablet contains 18.5 mg of calcium. How much
Galina-37 [17]

Answer:

740 mg of calcium is the correct answer

4 0
2 years ago
Other questions:
  • Dr. Watson combines 400 mL of detergent 800 ml of alcohol and 1500 mL of water how many liters of solution does he have
    8·1 answer
  • After a researcher adds 5 points to every score in a sample, the standard deviation is found to be s = 10. the original sample h
    10·1 answer
  • X+3y-2z=10, -x-2y+z=-7, 3x+9y-5z=28
    13·2 answers
  • WHen you have a graph, how do you find the vertex?
    14·2 answers
  • Calculate the volume and total surface area​
    12·1 answer
  • Marissa has a wool rug that has the shape of a regular octagon in her living room. The diameter of the incircle of the rug measu
    13·2 answers
  • 56 equals -10+ 2X what is 56 equals -10+ 2X what is X
    11·1 answer
  • What is a pure monopoly?
    15·1 answer
  • 5(4x+6) simplify and solve
    13·1 answer
  • A jet plane traveling at 400 mph overtakes a propeller plane traveling at 250 mph that had a 2​-hour head start. How far from th
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!