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# A company has 12 directors; one of them is president and

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Manager
Joined: 14 Mar 2007
Posts: 238
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Kudos [?]: 1 [0], given: 0

A company has 12 directors; one of them is president and [#permalink]  30 May 2007, 05:03
A company has 12 directors; one of them is president and another one of them is vice president. How many distinct commissions, with 6 directors, can be set up, as long as both the president and vice president are always on the commissions?

(A) 924
(B) 495
(C) 720
(D) 210
(E) 1260
Manager
Joined: 20 Dec 2004
Posts: 180
Followers: 2

Kudos [?]: 13 [0], given: 0

D
Since 2 of the members out of 6 are fixed. The no. of different commissions in which the rest 10 people can fill 4 seats is 10C4.

Hence 10C4=210
_________________

Regards

Subhen

Manager
Joined: 03 Mar 2007
Posts: 164
Followers: 1

Kudos [?]: 14 [0], given: 0

I get D as well.

10C4
Manager
Joined: 04 May 2007
Posts: 111
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Kudos [?]: 0 [0], given: 0

my first combo problem that i was able to tackle

you use 10C4 because vp and p have to be on the comittee they are a non issue. that leaves 10 people for 4 spots on a commision.

for some of the newer folks:

10 (n) things taken 4 (k) ways = n!/k!(n-k)!

=10!/4!6! <- get rid of 6!

10*9*8*7/4*3*2*1 <--- don't forget to always look for ways to make life easier for yourself 4*2=8 so get rid of 8

630/3 = 210
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# A company has 12 directors; one of them is president and

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