The total number of scoops of ice cream that Mary has is 3 cartons * 10 scoops = <<3*10=30>>30 scoops of ice cream.
Lucas, Danny and Connor will eat 2 scoops * 3 people = <<2*3=6>>6 scoops of ice cream.
Shannon will eat 2 * (1 vanilla + 1 strawberry) = <<2*(1+1)=4>>4 total scoops of ice cream.
Combined the kids will eat a total of 2 + 6 + 2 + 4 scoops = <<2+6+2+4=14>>14 scoops of ice cream.
Mary will have 30 scoops - 14 scoops = <<30-14=16>>16 scoops of ice cream remaining.
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