Did you see post #9 in this same thread?

Scientia and JFF are well grounded in questions like these.

Their complaint starts right here:

Courtesy of Wikipedia:

If f is a real-valued (or complex-valued) function, then taking the limit is compatible with the algebraic operations, provided the limits on the right sides of the equations below exist (the last identity only holds if the denominator is non-zero). This fact is often called the algebraic limit theorem.

bobbym wrote:

How would you judge this answer? And why?

The question itself and the replies given suggest this is wrong, but I would judge this answer correct. The following theorems are all easily proved:

The calculation shown follows from them.

]]>The second example checks out and on to the third...

Update:

The third example checks out! Ooooba oooba oooba, oooga ooog ooga! That means Wunderbar!

]]>That's good!

]]>I finally got the same answer you did. Then I had connection problems for 5 hours finally got back online.

]]>Okay, first problem checks out. On to the second one.

]]>My simulation answer is close: 0.0056

From the formula: 4162400 / C(52,8)

For your first example of 5,6,7,8 ( x x x 5 6 7 8 x ) I am getting a simulation answer about 1 / 10 th as large as predicted. What are you getting?

]]>... starting from 4th position

x x x 5 6 7 8 x

]]>Suppose we wanted to know the probability of sorted order to be 5 6 7 8, starting from 4th position:

Does this mean x x x x 5 6 7 8, where x are cards?

]]>