My numbers are correct. You are the one, who is wrong.
Are you sure that you're cosidering deck with 40/100 cards excluding hero?
My formula for 40 card deck is:
Chance of not drawing 3cc ally in first seven cards = C(36;7)*C(4,0)/C(40,7)=44,8%
Chance of drawing at least one 3cc ally in first seven cards=1-44,8%=55,2%
where C(n,k) is a number of k-combinations from a given set of n elements.
Good luck in finding mistake in your formula.
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