rvthryet wrote:
A Coach is filling out the starting lineup for his indoor soccer team. There are 10 boys on the team, and he must assign 6 starters to the following positions: 1 goalkeeper, 2 on defence, 2 in midfield, and 1 forward. Only 2 of the boys can play goalkeeper, and they cannot play any other positions. The other boys can each play any of the other positions. How many different groupings are possible?
A. 60
B. 210
C. 2580
D. 3360
E. 151200
We are given that there are 10 boys available to fill the following positions:
1 goalkeeper, 2 defenders, 2 midfielders, and 1 forward.
We are also given that only 2 of the boys can play goalkeeper.
Thus, we can select the goalkeeper in 2C1 = 2 ways.
We now have 8 boys left and need to select 2 defenders from those 8 boys:
8C2 = (8 x 7)/2! = 28 ways
We now have 6 boys left and need to select 2 midfielders:
6C2 = (6 x 5)/2! = 15 ways
We now have 4 boys left and need to select 1 forward:
4C1 = 4
Thus, the number of ways to select 6 starters is:
2 x 28 x 15 x 4 = 3,360
Answer: D
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