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# Paula and Quentin are two members of an eight-member committee.

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Manager
Joined: 18 Jun 2018
Posts: 232
Paula and Quentin are two members of an eight-member committee.  [#permalink]

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10 Sep 2018, 03:09
00:00

Difficulty:

15% (low)

Question Stats:

82% (01:04) correct 18% (01:06) wrong based on 22 sessions

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Paula and Quentin are two members of an eight-member committee. If the committee selects its president and secretary at random, and the same member cannot hold both positions, what is the probability that Paula is selected as president and Quentin is selected as secretary?

A) $$\frac{1}{64}$$

B) $$\frac{1}{56}$$

C) $$\frac{1}{49}$$

D) $$\frac{1}{36}$$

E) $$\frac{1}{24}$$
Intern
Joined: 02 Sep 2015
Posts: 42
Re: Paula and Quentin are two members of an eight-member committee.  [#permalink]

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10 Sep 2018, 03:26
Selecting paula out of 8 member committee: $$1C1/8C1$$ = $$1/8$$
Selecting Quentin out of 7 member committee: $$1C1/7C1$$ = $$1/7$$ since paula is already selected for presidency only 7 ppl are left for secretary
Selecting both: $$1/8 * 1/7$$ = $$1/56$$
CEO
Joined: 11 Sep 2015
Posts: 3122
Re: Paula and Quentin are two members of an eight-member committee.  [#permalink]

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10 Sep 2018, 04:41
Top Contributor
Bismarck wrote:
Paula and Quentin are two members of an eight-member committee. If the committee selects its president and secretary at random, and the same member cannot hold both positions, what is the probability that Paula is selected as president and Quentin is selected as secretary?

A) $$\frac{1}{64}$$

B) $$\frac{1}{56}$$

C) $$\frac{1}{49}$$

D) $$\frac{1}{36}$$

E) $$\frac{1}{24}$$

P(Paula becomes president and Quentin becomes secretary) = P(Paula becomes president) x P(Quentin becomes secretary)
= 1/8 x 1/7
= 1/56

Cheers,
Brent
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Re: Paula and Quentin are two members of an eight-member committee. &nbs [#permalink] 10 Sep 2018, 04:41
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