Solve by combination number, that is, select all different combination numbers of 3 from 7 different dishes. According to the formula of combination number, there are: c (7,3) = 7! / (3! * (7-3)! ) = 35。 Therefore, every three of the seven different dishes can be matched with 35 different combinations of dishes.

Combinatorial number is a concept in combinatorial mathematics, which refers to the number of combinations of m elements among n different elements, and is usually expressed by C(n, m) or (n chooses m). From N different elements, the combination number of M elements is equal to the arrangement number of M elements selected from N elements first (that is, A(n, m)=n! /(n-m)！ ), and then divided by the number of repetitions in each m tuple m! .