Party A and Party B played table tennis, winning four out of seven games. How many possible competitions are there?

40 possibilities.

To play seven games, the first six games should be the result of three wins and three losses. If these two people are A and B, there are three ways for A to win three games in the first three games, and there may be two ways for B to win the last game, so there may be 40 ways.

The calculation method of permutation and combination is as follows:

The arrangement A(n, m)=n×(n- 1). (n-m+ 1)=n! /(n-m)! (n is subscript and m is superscript, the same below)

Combination C(n, m)=P(n, m)/P(m, m) =n! /m! (n-m)! ;

For example:

A(4,2)=4! /2! =4*3= 12

C(4,2)=4! /(2! *2! )=4*3/(2* 1)=6