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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Ashley and Vinnie work on a sales staff with 8 other
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BTGmoderatorDC
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Jay@ManhattanReview
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Including Ashley and Vinnie, there are 10 salespeople.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
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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GMATGuruNY
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From the 10 people, 5 will be selected.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
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.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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Scott@TargetTestPrep
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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.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
Answer: C
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