A tricky math question...?

Question:A math question:

If there are 9 flavors of ice cream at a birthday party, and each child gets 2 scoops, and no flavor combination is repeated, what is the equation you would use to get the number of children at the party? I think the answer is 44, but I can't figure out the equation. And yes, all flavor combinations are used.

Answers:
use the formula for combinations:
n=9
k=2

C(9,2) = 9! / (2! (9-2)!)

when you cancel the 7! with the top, you get:

(9*8) / (2*1)
72/2 = 36 kids
9X8=72 NUMBER OF COMBOS.

72/2=36 ELIMINATES THE DUPLICATES LIKE VANILLA CHOCOLATE IS THE SAME AS CHOCOLATE VANILLA

THIS ASSUMES THAT 2 DIFFERENT FLAVORS ARE ON EVERY CONE.IF YOU ALSO ARE INCLUDING DUPLICATES LIKE CHOCOLATE-CHOCOLATE AND VANILLA-VANILLA ETC.ADD BACK 9 TO THE 36.
each kid can pick 1out of 9, and then 1 out of nine again, so the result is 81, 9 squared. (if a kid can't have 2 scoops of the same flavor, you cancel 9 combinations, and the result is 9*8=72)
however- this is double the answer- cause the combinations work both ways (choclate-strawberry/ strawberry-choclate) so the answer would be 72\2+9=45/

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