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

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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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