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There are k-2 members in a certain band, including Jim...

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by swerve » Tue Jan 30, 2018 5:38 am
There are k-2 members in a certain band, including Jim and Allan. Two members are to be selected to attend the Grammy awards ceremony. If there are 10 possible combinations in which Jim and Allan are not selected, what is the value of k?

A. 5
B. 9
C. 15
D. 18
E. 25

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
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There are k-2 members in a certain band, including Jim...

by regor60 » Tue Jan 30, 2018 6:29 am
swerve wrote:There are k-2 members in a certain band, including Jim and Allan. Two members are to be selected to attend the Grammy awards ceremony. If there are 10 possible combinations in which Jim and Allan are not selected, what is the value of k?

A. 5
B. 9
C. 15
D. 18
E. 25

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
If you find the combination formula confusing in this context, try using slots.

There are two slots available. Since you want to pick from the group excluding Jim and Allan, there are K-4 members to choose from.

Number of choices to fill the first slot is K-4. Therefore, the number of choices to fill the second slot is K-5.

Therefore, there are (K-4)*(K-5) groups of two, BUT this treats a group AB and BA as separate groups, which they are not, so need to divide by 2.

So, there are (K-4)*(K-5)/2 choices. The problem indicates that there are 10 combinations, therefore:

(K-4)*(K-5)/2 = 10 > K^2 - 9K + 20 =20

K^2 = 9K, therefore K=9, B
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by Scott@TargetTestPrep » Wed Jan 31, 2018 4:18 pm
swerve wrote:There are k-2 members in a certain band, including Jim and Allan. Two members are to be selected to attend the Grammy awards ceremony. If there are 10 possible combinations in which Jim and Allan are not selected, what is the value of k?

A. 5
B. 9
C. 15
D. 18
E. 25
We are given that there are k - 2 members in a band, including Jim and Allan. We are also given that 2 members are selected to attend the Grammy awards, not including Jim or Allan. We need to determine the value of k.

Since there are k - 2 members, if Jim and Allan are not selected, we have k - 2 - 2 = k - 4 members from which we can select. We can create the following equation to determine k:

(k - 4)C2 = 10

(k - 4)!/[2!(k - 4 - 2)!] = 10

(k - 4)!/[2!(k - 6)!] = 10

(k - 4)(k - 5)(k - 6)!/[2!(k - 6)!]

[(k - 4)(k - 5)]/2! = 10

k^2 - 9k + 20 = 20

k^2 - 9k = 0

k(k - 9) = 0

k = 0 or k = 9

Since k cannot be zero, k = 9.

Answer: B

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