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# Seven beads are in a bag: three blue, two red, and two

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Manager
Joined: 27 Aug 2004
Posts: 124
Location: US
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Seven beads are in a bag: three blue, two red, and two [#permalink]

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10 Sep 2004, 13:43
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Seven beads are in a bag: three blue, two red, and two green. If three beads are randomly drawn from the bag, what is the probability that they are not all blue?

A. 5/7
B. 23/24
C. 6/7
D. 34/35
E. 8/13
Director
Joined: 16 Jun 2004
Posts: 891
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10 Sep 2004, 13:53
D. 34/35

They are not all blue - means there could be '1 blue' or 'two blue' or 'all of other color'.

So, we have

(3C1*4C2)/7C3 + (3C2*4C1)/7C3 + 4C3/7C3 = 18/35 + 12/35 + 4/35 = 34/35.

Last edited by venksune on 10 Sep 2004, 14:12, edited 1 time in total.
Senior Manager
Joined: 05 Feb 2004
Posts: 290
Location: USA
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10 Sep 2004, 13:55
Prob of no blue = 1- (prob that all are blue)
= 1- 3C3/7C3 = 34/35............D!!
10 Sep 2004, 13:55
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