Let n=number of entrees on the menu
A "family dinner" is an un-ordered 4-entree subset of the set of n entrees on the menu; thus:
C(n,4) = 
n!
4! x (n-4)!
is the number
of possible
dinners
Using the above formula for various n:
C(4,4) = 1
C(5,4) = 5
C(6,4) = 15
C(7,4) = 35
   
C(8,4) = 70
C(9,4) = 126
C(10,4) = 210
C(11,4) = 330
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