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? Choose one
A) 60	B) 210	C) 2580	D) 3360	E) 151200
2C1 select 1 goalkeeper from 2 boys;   8C2 select 2 defense from 8 boys (as 2 boys can only play goalkeeper  10-2= 
<gadget id="calculator"> 10-2</gadget>
<output>8</output>
8);   6C2 select 2 midfield from 6 boys (as 2 boys can only play goalkeeper and 2 we've already selected for defense 10-2-2= 
<gadget id="calculator">10-2-2</gadget>
<output>6</output>
6);   4C1 select 1 forward from 4 boys (again as 2 boys can play only goalkeeper, 4 we've already selected for defense and midfield  10-2-4= 
<gadget id="calculator"> 10-2-4</gadget>
<output>4</output>
4)   Total # of selection=2C1*8C2*6C2*4C1=3360   Answer: 3360.
<result>D</result>
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?