GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
A certain academic department consists of 3 senior professors and 6 ju
[#permalink]
04 Oct 2021, 08:56
04 Oct 2021, 08:56
Expert Reply
00:00
Question Stats:
69% (01:04) correct
30% (02:07) wrong based on 13 sessions
Hide Show timer Statistics
A certain academic department consists of 3 senior professors and 6 junior professors. How many different committees of 3 professors can be formed in which at least one member of the committee is a senior professor? (Two groups are considered different if at least one group member is different.)
(A) 168
(B) 127
(C) 66
(D) 64
(E) 36
(A) 168
(B) 127
(C) 66
(D) 64
(E) 36
Re: A certain academic department consists of 3 senior professors and 6 ju
[#permalink]
04 Oct 2021, 20:10
04 Oct 2021, 20:10
1
The problems with atleast can be calculated as Total - none
We have \(3\) senior professors and \(6\) junior professors.
Total 9 prof. from which a committee of \(3\)
Total com. can be formed \(= 9\)C\(3 = 84\)
Let's consider when no senior professors are taken in the committee.
Total com. from \(6\) junior prof \(= 6\)C\(3 = 20\)
Hence, the no of committees when we will have at least \(1\) senior professor \(= 84 - 20 = 64\)
Answer D
We have \(3\) senior professors and \(6\) junior professors.
Total 9 prof. from which a committee of \(3\)
Total com. can be formed \(= 9\)C\(3 = 84\)
Let's consider when no senior professors are taken in the committee.
Total com. from \(6\) junior prof \(= 6\)C\(3 = 20\)
Hence, the no of committees when we will have at least \(1\) senior professor \(= 84 - 20 = 64\)
Answer D
Re: A certain academic department consists of 3 senior professors and 6 ju
[#permalink]
11 Jul 2022, 21:56
11 Jul 2022, 21:56
1
Way #2
Atleast one senior professor should be there,
--- atleast 1 equals more than or equal to 1 ---- in this case either 1 or 2 or 3. (since only 3 member community is to be formed).
We have 3 senior professors (S) and 6 junior professors (J).
1. 2 J + 1 S = 6c2 x 3c1 = 15 x 3 = 45
2. 1 J + 2 S = 6c1 x 3c2 = 6 x 3 = 18
3. 0 J + 3 S = 6c0 x 3c3 = 1 x 1 = 1
Total group can be formed = 45 +18 1 = 64
Answer D
_________________
Atleast one senior professor should be there,
--- atleast 1 equals more than or equal to 1 ---- in this case either 1 or 2 or 3. (since only 3 member community is to be formed).
We have 3 senior professors (S) and 6 junior professors (J).
1. 2 J + 1 S = 6c2 x 3c1 = 15 x 3 = 45
2. 1 J + 2 S = 6c1 x 3c2 = 6 x 3 = 18
3. 0 J + 3 S = 6c0 x 3c3 = 1 x 1 = 1
Total group can be formed = 45 +18 1 = 64
Answer D
_________________
