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22 Jan 2018, 09:32
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
43% (02:20) correct
57%
(02:28)
wrong
based on 21
sessions
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Not Attempted Yet
The host of a television debate show has to select a 4-member discussion panel out of a list of 22 willing candidates that includes 5 politicians and 6 businessmen. If the list includes candidates from at least 4 professions and no two members of the discussion panel are to be of the same profession, then in how many ways can the panel be constituted?
(1) The list includes 5 journalists and 2 authors
(2) The list includes only 1 profession from which there are fewer than 3 candidates
(1) The list includes 5 journalists and 2 authors
(2) The list includes only 1 profession from which there are fewer than 3 candidates
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22 Jan 2018, 10:03
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saswata4s
Hi..
We do not have to find answer, but we require to know is NUMBER of professions and members in each..
1) gives us 5 journalists and 2 authors.
So total 4 professions are known and they consist of 5+6+5+2=18..
So there are 4 more but they could be from different professions or from same or from 2 professions, so answers will be different everytime..
Insuff
2) only one profession has less than 3..
Insufficient..
Combined..
Less than 3 is 2 author so remaining have to be more than or equal to 3..
18 is given ... Only possiblity is all 22-18=4 are from same profession as they cannot be divided in two with each having 3 or more..
Sufficient... Number in each profession are 5,6,5,2,4 ..total 22
C
22 Jan 2018, 20:04
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chetan2u
Hi chetan2u,
Yes we got 5,6,5,2,4 as numbers in each profession.
But for 'how many possible ways', wouldn't the answer be different for different combinations of professions here?
Suppose 1 person is selected from first 4 professions: 5C1 + 6C1 + 5C1 + 2C1- So no. of possible ways =18
But if we select 1 person from last 4 professions: it will be 17.
Could you please tell where I am going wrong?
