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
Rodney is making three pizzas. The recipe says that, for one pizza, he needs 2 cups of flour, 2 teaspoons of instant active dry
Mamont248 [21]

Answer:

14 cups of flour.

Step-by-step explanation:

Rodney is making three pizzas.

The recipe says that for one pizza he needs flour = 2 cups

Rodney buy a bag of flour containing = 20 cups flour

Rodney needs flour for three pizzas = 3 × 2 = 6 cups

He will have left over flour after making the pizzas = 20 - 6

                                                                        = 14 cups of flour.

Rodney will have left over 14 cups of flour after making the pizzas.

6 0
3 years ago
Drag each equation to the model and situation it matches.
Alexxandr [17]

Answer:

YNW's ah family

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
there are 4800 plastic spoons in a case there 6 box3s of spoons in each case how many spoons are in each box
Slav-nsk [51]

Sorry if im wrong but i am pretty sure that is 266

3 0
3 years ago
Find the surface area of the square pyramid 8mm 6mm
bija089 [108]

Answer:

136 mm²

Step-by-step explanation:

A=a^{2} +2a\sqrt{\frac{a^{2} }{4} } +h^{2}

A=6^{2} +2(6)\sqrt{\frac{6^{2} }{4} } +8^{2}

A=36 +12\sqrt{\frac{36 }{4} } +64

A=36 +12\sqrt{9 } +64

A=36 +12(3)+64

A=36 +36+64

A = 136

5 0
3 years ago
A bird flies at a top speed of 20,000 meters per hour. The bird flies 30,000 meters without stopping. a. For how many hours did
bazaltina [42]

Answer:

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • A farmer is able to prepare 1/2 are of soil in 3 days. How long will it take him to prepare 2 1/4 acres of soil?
    8·1 answer
  • What is the solution for 75<-5(4x+1)
    12·2 answers
  • Brainlist at the first one to answer!!!!!! Plz........​ASAP!!!
    9·1 answer
  • Find the distance between the points (-10, 5) and (-8, -3).
    8·1 answer
  • ZD, ZE, and ZF are the perpendicular bisectors of ABC. Use that information to find the length of each segment. Not that the fig
    14·1 answer
  • Luis computed his taxable income for last
    8·1 answer
  • Help plz with this math problem. I’m so confused
    6·1 answer
  • Find the number if 20% of 64 is 10% of it?
    13·2 answers
  • A number y cubed plus x squared decreased by 7
    6·1 answer
  • A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, t
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!