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Yes, you are right about Liverpool which will get a ticket due to being in the top 4. This means that to create a crowd of English clubs we must wait for a feat from West Ham
What two other slots do you mean? Top 4 gets 4 slots. +1 slot if England oust Germany and another +1 slot if West Ham win the Europa League. I think the distribution of slots in the Europa League does not depend on the Champions League and those 2 clubs that are below the Champions League zone will receive their tickets. Well, there is still the option that Aston Villa will win the Conference League and then there will be 3 clubs from the Premier League in the Europa League.
It turns out that the maximum number could be as follows: 6 clubs in the Champions League, 3 clubs in the Europa League and the 10th club in the Conference League.
Good news for Chelsea!