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Coach Miller is filling out the starting lineup for his indoor soccer team. There are 10 boys on th team, and he must as

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Coach Miller is filling out the starting lineup for his indoor soccer team. There are 10 boys on th team, and he must as

by BTGmoderatorDC » Sat May 02, 2020 7:12 pm

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Coach Miller is filling out the starting lineup for his indoor soccer team. There are 10 boys on th team, and he must assign 6 starters to the following positions: 1 goalkeeper, 2 on defense, 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


OA D

Source: Princeton Review
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Re: Coach Miller is filling out the starting lineup for his indoor soccer team. There are 10 boys on th team, and he mus

by Jay@ManhattanReview » Wed May 06, 2020 12:10 am
BTGmoderatorDC wrote: ↑
Sat May 02, 2020 7:12 pm
 Coach Miller is filling out the starting lineup for his indoor soccer team. There are 10 boys on th team, and he must assign 6 starters to the following positions: 1 goalkeeper, 2 on defense, 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

OA D

Source: Princeton Review
No. of ways to select 1 goalkeeper = 2C1 = 2;
No. of ways to select 2 defense = 8C2 = 8.7/1.2 = 28; No. of players now left = 10 – 2 = 8
No. of ways to select 2 midfield = 6C2 = 6.5/1.2 = 15; No. of players now left = 8 – 2 = 6
No. of ways to select 1 forward = 4C1 = 4; No. of players now left = 6 – 2 = 4

The required no. of ways = 2*28*15*4 = 3,360

The correct answer: D

Hope this helps!

-Jay
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