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# Coach Miller is filling out the starting lineup for his

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Manager
Joined: 15 Jul 2004
Posts: 73
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Coach Miller is filling out the starting lineup for his [#permalink]  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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Let us make hay while the sun shines.
Don Quixote. Part i. Book. iii. Chap. xi.

VP
Joined: 30 Sep 2004
Posts: 1490
Location: Germany
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Kudos [?]: 80 [0], given: 0

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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Senior Manager
Joined: 19 Feb 2005
Posts: 488
Location: Milan Italy
Followers: 1

Kudos [?]: 10 [0], given: 0

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
VP
Joined: 30 Sep 2004
Posts: 1490
Location: Germany
Followers: 4

Kudos [?]: 80 [0], given: 0

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 ?
_________________

If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

Senior Manager
Joined: 19 Feb 2005
Posts: 488
Location: Milan Italy
Followers: 1

Kudos [?]: 10 [0], given: 0

sorry, I miscalculated.
Happy to see different ways to approach the same problem
VP
Joined: 30 Sep 2004
Posts: 1490
Location: Germany
Followers: 4

Kudos [?]: 80 [0], given: 0

thearch wrote:
sorry, I miscalculated.
Happy to see different ways to approach the same problem

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If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

Intern
Joined: 29 Mar 2005
Posts: 38
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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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Senior Manager
Joined: 19 Feb 2005
Posts: 488
Location: Milan Italy
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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.
VP
Joined: 13 Jun 2004
Posts: 1123
Location: London, UK
Schools: Tuck'08
Followers: 7

Kudos [?]: 30 [0], given: 0

I found D doing 8P5/2!
Interesting...Honnestly, I have no idea what's the logic behind it
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