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A certain academic department consists of 3 senior professors and 6 j

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Carcass
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A certain academic department consists of 3 senior professors and 6 j [#permalink] New post   30 Sep 2021, 02:47
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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
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D
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KarunMendiratta
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Re: A certain academic department consists of 3 senior professors and 6 j [#permalink] New post   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


Number of ways of picking 1 Senior and 2 Juniors = (3C1)(6C2)=45

Number of ways of picking 2 Senios and 1 Junior = (3C2)(6C1)=18

Number of ways of picking all 3 Seniors = (3C3)=1

Total ways = 45 + 18 + 1 = 64

Hence, option D
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Re: A certain academic department consists of 3 senior professors and 6 j [#permalink] New post   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
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Re: A certain academic department consists of 3 senior professors and 6 j [#permalink]
25 Jun 2022, 23:17
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