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# A certain club has 10 members, including Harry. One of the

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Senior Manager
Joined: 14 Aug 2006
Posts: 365
Followers: 1

Kudos [?]: 3 [0], given: 0

A certain club has 10 members, including Harry. One of the [#permalink]  24 Aug 2006, 18:20
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A certain club has 10 members, including Harry. One of the 10 members is to be chosed at random to be the president, one of the remaining 9 members is to be chosed at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will either be the secretary or the member chosen to be the treasurer?

A 1/720
B 1/80
C 1/10
D 1/9
E 1/5

Edit: For the latest and most complete discussion of this Official Guide 12 Question, please see:
a-certain-club-has-10-members-including-harry-40987.html
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Senior Manager
Joined: 11 May 2006
Posts: 260
Followers: 1

Kudos [?]: 6 [0], given: 0

E

p(H as secretary) = 9/10 * 1/9 = 1/10
p(H as treasurer) = 9/10 * 8/9 * 1/8 = 1/10

p(H as secretary or treasurer) = 1/10 + 1/10 = 1/5
Director
Joined: 28 Dec 2005
Posts: 758
Followers: 1

Kudos [?]: 8 [0], given: 0

Total permutations = 10P3 = 10!/7!

Permutations when Harry is Sec = 9P2
Permutations when Harry is Trea = 9P2

Required Prob. = 2. (9!/7!)/(10!/7!) = 2/10 = 1/5
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