Permutations and Combination

Question

When a fair dice is tossed, it can result in a score of 1,2,3,4,5, or 6. How many different results can be obtained from three dice which are tossed simultaneously.

Answer 1

A result is the sum of the numbers on the three die.  The smallest result is when all three dice have a value of one and the result is 3.  The largest result is when all three dice have a value of six and the result is 18.  Any result between 3 and 18 are possible.  The number of different results is 16: 3, 4, 5, ..., , 17, 18

Answer 2

when 2 dice are tossed there are 36 sum in the sample space (6^2)

when 3 dice are tossed each of the 36 sums can be paired with 1, 2, 3, 4, 5, or 6

therefore 36*6=216 sums are in the sample space (6^3)

you mention the word different

if you toss 2 dice you can get 3 and 4, 4 and 3, 2 and 5, 5 and 2, 1 and 6, 6 and 1, which are all part of the sample space

 

Answer 3

6³ is the answer; the question does not ask about total, which indeed is one of the integers from 1 to 18.

 

ANSWER: 216...e.g. think about the 3 dies as A,B&C; several outcomes are

1,1,1

1,1,2

1,1,3

1,1,4

1,1,5

1,1,6

and then we get into 

2,1,1
2,1,2
2,1,3
2,1,4
2,1,5
2,1,6 and then when we have exhausted all of the possibile configurations with different A values, we 

begin again:

2,1,1

2,1,2

etc.

 

These are all different (but not in their totals)...so correct answer really is 6³.