Rolling a single die

I've done a Monte-Carlo simulation on this which suggests the probability of getting all the numbers at least once is about 0.356.

I selected 11 numbers uniformly and randomly from the digits 1 to 6.   I then looked to see if all the digits from 1 to 6 were present.  If they were all present I increased a running total (that started at zero) by 1; if they weren't all present I didn't increase the running total.  I repeated this two million times and calculated the probability as  running total/two million.

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You wouldn't when would you ever need to know such a thing

1-(1-1/6)^11

How do you come to that calculation though? Thank! (So it would be ~86%?)

Re asked here

http://web2.0calc.com/questions/probability_882