If there are 250 legos in a box, how many possible combinations of legos are possible in a lego tower if a tower can be anywhere from 1 to 250 legos tall.

We suppose that the 250 legos are different between them, so we have that:

for 1 lego, we have 250 combinations.

For two legos, we have 250 for the first lego, and 249 for the second lego, this is 250*249 combinations.

for 3 legos, we will have 250*249*248 probabilities.

and so on:

Then the total number of combinations will be:

C = 250 + 250*249 + 250*249*248 +

   = 250*(1 + 249*(1 + 248*(1 + 247*(

The number that is kinda hard to calculate, even in a calculator

this summation can be written as:

∑(250)!/(249 - n)!

wich is a big big big number

for the free

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