Distribution of suits question

[SA125]

What is the likely distribution of suits for a full ring 10 player holdem game before the flop?

My basic math skills say 4 suits into 20 cards gives an average of 5 per suit per deal.

If that's true and you hold 2 of the same suit, when you hit another 2 of your suit on the flop that means the average number of your suit to be out would be 7.

I'd really appreciate any light you can shed on that. Thanks.