In a certain British soccer pool, the objective is to pick games that end in a tie. The ticket buyer picks 8 games from a list of 45 or more. For each of these games,

if the teams tie, the player gets 3 points, if the visiting team wins, they get 2 points, and if the home team wins, they get 1.5 points. The entry with the highest point total wins.

Assume that for each game, the probability of the home team’s winning is 0.5, the probability of the visiting team’s winning is 0.4, and the probability of a tie is 0.1.

Determine the probability that the total points for an entry will be 22 or higher.