Can anyone please answer this higher probability question?

An arithmetic progression is a sequence of numbers where the difference between each number is a constant.

We have 25 sequences that are ascending:

1 2 3

1 3 5

1 4 7

1 5 9

1 6 11

2 3 4

2 4 6

2 5 8

2 6 10

3 4 5

3 5 7

3 6 9

3 7 11

4 5 6

4 6 8

4 7 10

5 6 7

5 7 9

5 8 11

6 7 8

6 8 10

7 8 9

7 9 11

8 9 10

9 10 11

So we have 25 sequences that work, however, You didn't indicate whether the order

of the draw makes a difference. I'll assume that these numbers can be rearranged into

a correct order even if the middle number was drawn first or last.

So each of these sequences represent six distinct draws. For eample:

1 2 3

2 3 1

3 2 1

1 3 2

3 1 2

2 1 3

So there are really, 25 X 6 ways to find a geometric sequence, or 150 specific sequences that meet the requirments..

The next question is how many total sequences can be drawn. There are 11 ways to draw the first number, 10 ways to draw the second, and 9 ways to draw the last. There are 990 ways to draw numbers 150/990 = .1515...

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