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
vfiekz [6]
3 years ago
11

A fair die is rolled four times. Find the probability that all four rolls show different numbers

Mathematics
2 answers:
storchak [24]3 years ago
5 0

umber of possible outcomes = 6^4 = 1296

Probability of favorable outcomes = 126/1296=7/72


tensa zangetsu [6.8K]3 years ago
4 0

Number of such outcomes, in which each number is no less than the preceding number, will be equal to number of ways of selecting 4 numbers from 6, with replacement; without considering order!


Why?


Lets choose any such set of size 4, say {2, 1, 1, 3}. we can sort it to get a sequence {1,1,2,3} which is one of our desired outcomes. So each such sorted sequence corresponds to one selection of size 4, with replacement and without considering order.


Number of such selections will be equal to number of solutions of following equation:


x1 + x2 + x3 + x4 + x5 + x6 = 4


where:


x1: number of 1 in the selections


x2: number of 2s in the selection


.


.


x6: number of 6s in the selection


Number unique solutions of such equation = 9 choose 5 = 126


(For more details on this see : Unordered sampling with replacement )


Number of possible outcomes = 6^4 = 1296


Probability of favorable outcomes = 126/1296=7/72



You might be interested in
Factor completely 4x^5-20x^3
nikdorinn [45]

Answer:

<em>4x^3(x^2 - 5)</em>

Step-by-step explanation:

First, try to factor a common factor.

GCF of 4 and -20 is 4.

GCF of x^5 and x^3 is x^3.

Factor out 4x^3.

4x^5 - 20x^3 =

= 4x^3(x^2 - 5)

3 0
3 years ago
How to graph y = 2|x + 3| - 4
mr_godi [17]

The x-intercepts and the y-intercepts of the function is that determines the graph is:

  • x-intercepts = (-5,0) and (-1,0)
  • y-intercepts = (0,2)

<h3>How do we graph the function y = f(x) of an absolute equation?</h3>

The function of an absolute equation can be graphed by determining the values of x-intercepts and the y-intercepts of the function.

From the given equation:

y = 2|x+3| - 4

To determine the y-intercepts, we need to set the values of x to zero, and vice versa for x-intercepts.

By doing so, the x-intercepts and the y-intercepts of the function is:

  • x-intercepts = (-5,0) and (-1,0)
  • y-intercepts = (0,2)

Therefore, since we know the x and y-intercepts, the graph of the absolute value can be seen as plotted below.

Learn more about determining the graph of an absolute equation here:

brainly.com/question/2166748

#SPJ1

8 0
1 year ago
Write (-3)^4 in standard form
Olenka [21]

Answer: 81

Step-by-step explanation: Because, (-3)^4=-3*-3*-3*-3=-(-81)=81

3 0
3 years ago
WORTH 20 POINTS PLS HELP!
scZoUnD [109]

Answer:80ft

Step-by-step explanation:

4 0
3 years ago
Jones Co. pays its employees on a graduated commission scale: 2% on first $30,000; 3% on sales from $30,000 to $60,000; and 5% o
Gnesinka [82]
We need to separate his total earnings out into the different categories:

Category 1 (2%): 30,000
Category 2 (3%): 60,000-30,000 = 30,000
Category 3 (5%): 92,000-60,000 = 32,000

To calculate a percentage we multiply by that percentage divided by 100.
Now we can work out the commissions:
1) 30,000*0.02 = $600
2) 30,000*0.03 = $900
3) 32,000*0.05 = $1600

Adding these together, we get $3100
3 0
3 years ago
Other questions:
  • -12 - 8 - (-20) = A.0 B.16 C.-40 D.40
    5·1 answer
  • The cost of going to the big playland park for a family is given by C = 15x + 50, where C represents the cost and x represents t
    7·1 answer
  • Helppp what is the correct answer and why?
    13·1 answer
  • What are the steps to get the product of(7x-6)^2
    11·2 answers
  • Explain the process for determining sales tax and total purchase price
    7·1 answer
  • Determine whether the equation represents direct, inverse, joint, or combined variation.
    14·1 answer
  • Solve please. Correctly<br> -2x + 5x = 3x - 3
    5·2 answers
  • Pls help me I’ll mark brainliest!!
    11·2 answers
  • The map shows the location of the airport and a warehouse in a city. Though not displayed on the map, there is also a factory 88
    5·2 answers
  • A rocket is shot off from a launcher. The accompanying table represents the height of the rocket at given times, where x is time
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!