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A certain academic department consists of 3 senior professors and 6 j
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30 Sep 2021, 02:47
30 Sep 2021, 02:47
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24% (01:29) wrong based on 25 sessions
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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
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Re: A certain academic department consists of 3 senior professors and 6 j
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05 Oct 2021, 22:01
05 Oct 2021, 22:01
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Carcass wrote:
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
Number of ways of picking 1 Senior and 2 Juniors = \((^3C_1)(^6C_2) = 45\)
Number of ways of picking 2 Senios and 1 Junior = \((^3C_2)(^6C_1) = 18\)
Number of ways of picking all 3 Seniors = \((^3C_3) = 1\)
Total ways = 45 + 18 + 1 = 64
Hence, option D
Re: A certain academic department consists of 3 senior professors and 6 j
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25 Jun 2022, 23:17
25 Jun 2022, 23:17
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we can also use the at least method for solving this problem. Atleast 1 object = total outcome - (none of the expected items occur)
First, to choosing 3 professors from total 9 professor is, = 9C3 = 84 ways
second, choosing 3 professors only from junior professors is, 6c3 = 20 ways
so, atleast for choosing 1 senior professor is= 84-20= 64 ways
First, to choosing 3 professors from total 9 professor is, = 9C3 = 84 ways
second, choosing 3 professors only from junior professors is, 6c3 = 20 ways
so, atleast for choosing 1 senior professor is= 84-20= 64 ways
