Probability of selecting pipes from a batch

Hi all,

I have a problem at work regarding probability;

I have data for one batch 1200 lengths of pipe. I need to calculate the probability of 6 pipes being selected from the batch at random and the summation of these lengths of pipe not exceeding 74.1m long.

Now I could create a huge spread sheet of all the possible outcomes of selecting 6 of the 1200 pipes at random but that's way to long winded.

Is there a shorter method? creating a function and integrating between intervals?

Any help would be much appreciated.