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# Coach Miller is filling out the starting lineup for his

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Manager
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Coach Miller is filling out the starting lineup for his [#permalink]

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09 Apr 2005, 00:19
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Coach Miller 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
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 2,580
D 3,360
E 151,200
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09 Apr 2005, 01:20
take 1 out of 2 => 2c1
take 5 out of 8 => 8c5
that are the 6 starters

then out of the 6 starters take 1 as goalkeeper and 2 as defense (=>5c2) and 2 as midfield (=>3c2) and 1 as forward

=> 2c1*8c5*1*5c2*3c2*1
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09 Apr 2005, 01:28
BTW, my reasoning:
2 possibilities for gk
8c2 for position 1
6c2 for position 2
4c1 for position 3
which is= 3360
D 3,360
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09 Apr 2005, 01:36
thearch wrote:
BTW, my reasoning:
2 possibilities for gk
8c2 for position 1
6c2 for position 2
4c1 for position 3
which is= 3360
D 3,360

why? 2c1=2 8c5=56 1=1 5c2=10 3c2=3 1=1 multiply all = 3360, is it ?
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09 Apr 2005, 01:42
sorry, I miscalculated.
Happy to see different ways to approach the same problem
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09 Apr 2005, 01:50
thearch wrote:
sorry, I miscalculated.
Happy to see different ways to approach the same problem

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11 Apr 2005, 12:31
What does 8c1 mean? I see the #c# a lot in these forums on probability questions, but don't know what it refers to. Can someone please explain? thx
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11 Apr 2005, 12:37
8c2 stands for 8!/(2!6!)
that is the general formula for combinations n!/(n-r!r!).
You can find more in various stickies posted at the top of the Math forum.
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11 Apr 2005, 19:22
I found D doing 8P5/2!
Interesting...Honnestly, I have no idea what's the logic behind it
11 Apr 2005, 19:22
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