Answer: To calculate the number of different ways to choose players for each position, we can use the concept of combinations. The number of ways to choose players without considering the positions is given by the combination formula:
C(n, r) = n! / (r!(n - r)!)
where n is the total number of players and r is the number of players to be chosen for a specific position.
In this case, we have:
Choosing 1 goalie out of 30 people: C(30, 1) = 30! / (1!(30 - 1)!) = 30.
Choosing 5 defenders out of the remaining 29 people (after selecting the goalie): C(29, 5) = 29! / (5!(29 - 5)!) = 8,870.
Choosing 6 midfielders out of the remaining 24 people (after selecting the goalie and defenders): C(24, 6) = 24! / (6!(24 - 6)!) = 13,545.
Choosing 3 forwards out of the remaining 18 people (after selecting the goalie, defenders, and midfielders): C(18, 3) = 18! / (3!(18 - 3)!) = 816.
To find the total number of ways to choose players for each position, we multiply the results together:
Total ways = 30 * 8,870 * 13,545 * 816 = 27,160,146,800.
Therefore, there are 27,160,146,800 different ways to choose 1 goalie, 5 defenders, 6 midfielders, and 3 forwards from a group of 30 people.
Step-by-step explanation: btw theres not 5 defenders theres *3*