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Ashley and Vinnie work on a sales staff with 8 other

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Ashley and Vinnie work on a sales staff with 8 other

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Ashley and Vinnie work on a sales staff with 8 other salespeople. If five members of the staff will be chosen at random to attend a sales workshop, what is the probability that both Ashley and Vinnie will be chosen?

A. 1/10

B. 3/28

C. 2/9

D. 1/4

E. 1/2

OA C

Source: Veritas Prep

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BTGmoderatorDC wrote:
Ashley and Vinnie work on a sales staff with 8 other salespeople. If five members of the staff will be chosen at random to attend a sales workshop, what is the probability that both Ashley and Vinnie will be chosen?

A. 1/10

B. 3/28

C. 2/9

D. 1/4

E. 1/2

OA C

Source: Veritas Prep
There are 10C5 = 10!/(5! x 5!) = (10 x 9 x 8 x 7 x 6)/(5 x 4 x 3 x 2) = 2 x 9 x 2 x 7 = 252 ways to choose 5 people from 10. Assuming Ashley and Vinnie are already chosen, there are only 3 spots left for the other 8 people, and the number of ways to choose 3 people from 8 is 8C3 = 8!/(3! x 5!) = (8 x 7 x 6)/(3 x 2) = 56. Therefore, the probability is 56/252 = 8/36 = 2/9.

Answer: C

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BTGmoderatorDC wrote:
Ashley and Vinnie work on a sales staff with 8 other salespeople. If five members of the staff will be chosen at random to attend a sales workshop, what is the probability that both Ashley and Vinnie will be chosen?

A. 1/10

B. 3/28

C. 2/9

D. 1/4

E. 1/2
From the 10 people, 5 will be selected.
Thus, P(Ashley is selected) = 5/10.
From the 9 remaining people, 4 will be selected.
Thus, P(Vinnie is selected) = 4/9.
To combine these probabilities, we multiply:
5/10 * 4/9 = 2/9.

The correct answer is C.

Similar problem:
https://www.beatthegmat.com/probability-question-adam-selected-and-not-karen-t272268.html

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BTGmoderatorDC wrote:
Ashley and Vinnie work on a sales staff with 8 other salespeople. If five members of the staff will be chosen at random to attend a sales workshop, what is the probability that both Ashley and Vinnie will be chosen?

A. 1/10

B. 3/28

C. 2/9

D. 1/4

E. 1/2

OA C

Source: Veritas Prep
Including Ashley and Vinnie, there are 10 salespeople.

Number of ways of choosing ANY 5 members out of 10 = 10C5;
Number of ways of choosing 5 members out of 10 such that 2 of them are Ashley and Vinnie = 2C2 * 8C3 = 8C3;

Probability that both Ashley and Vinnie will be chosen = 8C3 / 10C5 = 2/9

The correct answer: C

Hope this helps!

-Jay
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Manhattan Review GMAT Prep

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