Real-life Ballot problem

Wonder if anyone can help me.

There has been an oversubscription of applications for tickets for a major sporting event so the organisers have announced a ballot.

There are 6000 tickets and 24000 applicants so a 25% chance of success

(22.9% in the real life situation with 5918/25800)

On announcement of the results of the random non-biased computerised ballot, many large groups of friends are finding they have all been unsuccessful, or as part of the group successful at ratios well below 25%. They all applied to the ticket ballot independently with no method of the organiser knowing the applications were linked in any way by friendship, workplace, family relations.

What are the chances if everything is entirely random of groups of friends having success rates of:

0/10, 0/20, 0/30, 0/40
1/10, 1/20, 1/30, 1/40
2/10, 2/20, 2/30, 2/40
3/10, 3/20, 3/30, 3/40
4/10, 4/20, 4/30, 4/40

I assume there is a formula that I can plug the above numbers into, to allow me to show that a series of success rates of the likes of 1/40, 2/53, 0/20, 1/16 are highly improbable?

(to expand some people think the ballot hasn't been entirely random and/or the success rate of 25% is not accurate given all these very low success rates)

thanks in advance for any help.