Question

Three fair dice are tossed. What is the probabiligy that the three numbers turned up can be arranged to form an arithmetic sequence?

Answer 1

I have an answer but I'm looking for someone who can explain how to do it

Answer 2

@Zarkon I am waiting for your explanation. Please, explain us.

Answer 3

list out some possible arithmetic sequences...in monotone order...there aren't that many. then permute them to get the total number

Answer 4

Do we have to raise to the power of 3 ? I meant let say 1-2-3 as one possibility, and 1 for dice 1, 2 for dice 2, and 3 for dice 3. The order can apply for 1 for dice 2, 2 for dice 1 and 3 for dice 3. So that we need to raise the possibility to 3, right?

Answer 5

1,2,3
1,3,2
2,1,3
2,3,1
3,1,2
3,2,1

3! possibilities for 1,2,3

Answer 6

Got you. Thanks for explanation.

Answer 7

132 is an arithmetic sequence?

Answer 8

No, I think one sequence can either increase or it can decrease. It can't do both.

Answer 9

" CAN be arranged to form an arithmetic sequence"

Answer 10

132 can be arranged as 123

Answer 11

123, 135, 234, 246, 345, 456 , so are you saying there would be 36?

Answer 12

there are more

Answer 13

not 3 factorial for each of those groups?

Answer 14

111,222,...,666

are arithmetic (common difference of 0)

Answer 15

Right so 42?

Answer 16

yes

Answer 17

The way to find the total number of different combos though?

Answer 18

you just did

Answer 19

No those were possible arithmetic sequences. I need a probability, so 42/x

Answer 20

6 possibilities for each die

\(6^3=216\) total

Answer 21

then there's the fact that 116 is the same as 161 and 611

Answer 22

and...

Answer 23

out of the 216 possible ways to roll the dice we found 42 that can be arranged into an arithmetic sequence

Answer 24

Okay, thank you.