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A four-person leadership committee is to be chosen from a
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30 Dec 2017, 13:18
30 Dec 2017, 13:18
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Question Stats:
72% (01:03) correct
27% (01:32) wrong based on 88 sessions
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A four-person leadership committee is to be chosen from a student council that consists of seven juniors and five seniors. Q is the total number of different leadership committees that include three seniors and one junior.
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
Q |
75 |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Drill 1
Question: 11
Page: 561
Question: 11
Page: 561
Re: A four-person leadership committee is to be chosen from a
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07 Jan 2018, 18:24
07 Jan 2018, 18:24
1
Expert Reply
Explanation
Start by finding out how many groups of three seniors can be chosen from the five seniors: \(\frac{5}{3} \times \frac{4}{2} \times \frac{3}{1}=10\).
Next, multiply that total by the number of individual juniors with which those groups can be paired (7) to form the full committee: 10 × 7 = 70. Quantity B is greater.
Start by finding out how many groups of three seniors can be chosen from the five seniors: \(\frac{5}{3} \times \frac{4}{2} \times \frac{3}{1}=10\).
Next, multiply that total by the number of individual juniors with which those groups can be paired (7) to form the full committee: 10 × 7 = 70. Quantity B is greater.
Re: A four-person leadership committee is to be chosen from a
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07 Jan 2018, 23:29
07 Jan 2018, 23:29
J=7
S=5
Since we need 3J and 1S, 5C3 = 5*4*3!/2!3!=10 and 7C1=7, hence 7*10=70.
Therefore B is greater
S=5
Since we need 3J and 1S, 5C3 = 5*4*3!/2!3!=10 and 7C1=7, hence 7*10=70.
Therefore B is greater
