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A committee of four people is to be selected from a group consisting o

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A committee of four people is to be selected from a group consisting o [#permalink] New post   25 Oct 2021, 05:21
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A committee of four people is to be selected from a group consisting of five women and four men.


Quantity A
Quantity B
The probability that two women and two men are on the committee
The probability that three women and one man are on the committee



A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
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A
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Re: A committee of four people is to be selected from a group consisting o [#permalink] New post   26 Oct 2021, 20:16
\(4\) people to select from \(5\) women & \(4\) men

Qt A

Prob of two women & two men \(= \frac{5C2 * 4C2}{9C4} = \frac{30}{63}\)

Qt B

Prob of three women & one men \(= \frac{5C3 * 4C1}{9C4} = \frac{20}{63}\)

Qt A > Qt B

Answer A
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Re: A committee of four people is to be selected from a group consisting o [#permalink] New post   24 Jul 2022, 23:23
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Using probability method
QA: (4/9 × 3/8 × 5/7 × 4/6) × 4!/2!2!
QB: (5/9 × 4/8 × 3/7 × 4/6) × 4!/3!1!
QA: 6
QB: 4
Therefore A is greater

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Re: A committee of four people is to be selected from a group consisting o [#permalink]
24 Jul 2022, 23:23
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