Probability (hard)...?

Question

1,2,3 there are 16 1,2,3's in a lottery, I guess that all 16 will turn out

1,2,3 as number 1. What are the odd's that I get all 16 right?

1,2,3 and what are the odds the get 15,14, 13, 12, 11, 10 correct? ty.

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

Answer 1

i don't get it  need more info

Answer 2

If I understand this correctly, there are 16 "numbers", each number can either be "1, 2, or 3".  Also I would assume order matters here as in:

{1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2}

is NOT equal to

{1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1}

Assuming these things:

The probability of all 16 being "1" is (1/3)^16 =  1 in 43,046,721

This is also the same probability of you getting all 16 correct.

15 correct:

[16/1]*[(2/3)]*[(1/3)^15] = 1 in 1,345,210

14 correct:

[16*15/2/1]*[(2/3)^2]*[(1/3)^14]= 1 in 89,681

13 correct:

[16*15*14/3/2/1]*[(2/3)^3]*[(1/3)^13]= 1 in 9,609

The same pattern works for 12, 11, and 10 correct...the answers are:

12 correct:  1 in 1,478

11 correct:  1 in 308.0

10 correct:   1 in 84.0

Answer 3

By ignoring all the 1,2,3's you wrote, I think I figured out your question.

The answer that all 16 gambles turn out as 1 would be

(1/3)   *there's a third of a chance it is a 1*  to the power of 16.

So (1/3) ^ 16.

Odds of 15 changes, it would become 15C1 * (2/3) * (1/3) ^ 15.

You can calculate that.

There are many sites you can search to explain this, it's not very complex.