Final answer:
To find the number of ways to form a group of 4 players with exactly 1 district level player out of 8 district and 12 state level players, calculate the combination of 8 choose 1 and 12 choose 3, yielding 1,760 different ways.
Step-by-step explanation:
The student is asking about the number of ways a group of 4 players can be formed from a total of 20 players (12 state level and 8 district level) such that the group contains exactly 1 district level player. This is a combinatorial problem involving combinations since the order in which the players are selected does not matter.
To solve this, we select 1 player from the 8 district level players and then select 3 players from the 12 state level players. The number of ways to choose 1 district level player is 8 choose 1 (notated as 8C1), and the number of ways to choose 3 state level players is 12 choose 3 (notated as 12C3). The total number of ways to form the group is the product of these two quantities.
C(8,1) * C(12,3) = 8 * 220 = 1760.
So, there are 1760 ways to form the group.
Thus, the calculation is: 8C1 × 12C3 = 8 × (12 × 11 × 10) / (3 × 2 × 1) = 8 × 220 = 1,760 different ways to form the group.