5.086 In how many ways can the players of two football teams be arranged in a single row so that no two players from the same team stand next to each other?
Solution. All players of the first team must occupy only even (or only odd) positions in the line. The number of ways to distribute the players of one team to even (or odd) positions is 11! (the number of permutations of 11 elements). Therefore, the total number of ways to form a line where all players of the first team occupy odd positions and players of the second team occupy even positions is (11!)^2. A similar result is obtained if the first team occupies even positions in the line. Therefore, the total answer is 2 \cdot(11!)^2.

Answer: 2 \cdot(11!)^2.