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The host of a television debate show has to select a 4-member

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The host of a television debate show has to select a 4-member  [#permalink]

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New post 22 Jan 2018, 09:32
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41% (01:16) correct 59% (01:27) wrong based on 37 sessions

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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

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Re: The host of a television debate show has to select a 4-member  [#permalink]

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New post 22 Jan 2018, 10:03
saswata4s wrote:
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



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
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: The host of a television debate show has to select a 4-member  [#permalink]

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New post 22 Jan 2018, 20:04
chetan2u wrote:
saswata4s wrote:
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



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



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?
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Re: The host of a television debate show has to select a 4-member  [#permalink]

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New post 22 Jan 2018, 21:53
1
kkrrsshh wrote:
chetan2u wrote:
saswata4s wrote:
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



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



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?


Hi..
Our answer "all possible ways" will include all of these..
So if there are 5 professions, you can choose 4 out of them in 5C4 ways, that is 5 ways..
So find POSSIBLE ways for each combination and ADD all of these to get the final answer.
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: The host of a television debate show has to select a 4-member  [#permalink]

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New post 23 Jan 2018, 19:51
Oh Yes.. Got it. Thanks

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.


If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
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Re: The host of a television debate show has to select a 4-member &nbs [#permalink] 23 Jan 2018, 19:51
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The host of a television debate show has to select a 4-member

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