From a seven-member dance group, four will be chosen at

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

From a seven-member dance group, four will be chosen at

by BTGmoderatorLU » Wed Jul 03, 2019 2:33 pm

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Source: Veritas Prep

From a seven-member dance group, four will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the seven members, what is the probability that both will be chosen to volunteer?

A. \(1/21\)
B. \(1/7\)
C. \(4/21\)
D. \(2/7\)
E. \(3/7\)

The OA is D

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Source: Beat The GMAT — Problem Solving | Wed Jul 03, 2019 2:33 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Wed Jul 03, 2019 10:48 pm

BTGmoderatorLU wrote:Source: Veritas Prep

From a seven-member dance group, four will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the seven members, what is the probability that both will be chosen to volunteer?

A. \(1/21\)
B. \(1/7\)
C. \(4/21\)
D. \(2/7\)
E. \(3/7\)

The OA is D

Number of ways such that any of the 4 dances are chosen randomly = 7C4;
Number of ways such that Kori and Jason are selected and any of the remaining 2 dances are chosen randomly = 5C2;

Required probability = 5C2 / 7C4 = 2/7

The correct answer: D

Hope this helps!

-Jay
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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

by swerve » Thu Jul 04, 2019 11:43 am

Hi, you can try as follows:

There are 7 members including Kori and Jason. We are to find the probability of choosing these two if we are selecting 4 out of these 7.
Way to choose 4 out of \(7= 7C4=35\).

Now two out of 4 are Kori and Jason. The remaining 2 are to be chosen from remaining 5. (K and J are not included as they are already chosen).

So \(5C2=10\).
prob \(=10/35 \Rightarrow\) D

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Jul 06, 2019 5:08 pm

BTGmoderatorLU wrote:Source: Veritas Prep

From a seven-member dance group, four will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the seven members, what is the probability that both will be chosen to volunteer?

A. \(1/21\)
B. \(1/7\)
C. \(4/21\)
D. \(2/7\)
E. \(3/7\)

The OA is D

We are given that from 7 members, 4 people will be selected for a dance team. We need to determine the probability that both Kori and Jason will be selected.

Let's first determine the total number of ways to select 4 people from a group of 7 people.

The number of ways to select 4 people from a group of 7 is:

7C4 = 7! / (3! x 4!) = (7 x 6 x 5 x 4) / 4! = (7 x 6 x 5 x 4) / (4 x 3 x 2 x 1) = 7 x 5 = 35

Next, we need to determine the number of ways the group can be selected when both Kori and Jason are selected. Since they both must be selected, there are 5 remaining people for the 2 remaining spots. We can select 2 people from 5 in the following ways:

5C2 = 5! / (3! x 2!) = (5 x 4) / 2! = 20/2 = 10

Thus, the probability of creating a 4-person dance team that includes both Kori and Jason is 10/35 = 2/7.

Answer: D

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