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

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

30 May 2007, 06:03

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

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30 May 2007, 06:11

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
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Subhen

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30 May 2007, 06:37

I get D as well.

10C4

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30 May 2007, 08:50

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

[#permalink] 30 May 2007, 08:50

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

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

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

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