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A company interviewed 5 applicants each for the posts of the Director

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Director
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A company interviewed 5 applicants each for the posts of the Director  [#permalink]

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New post 14 Apr 2019, 07:30
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Question Stats:

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A company interviewed 5 applicants each for the posts of the Director and the President. If Jack and Jill were the only applicants who were interviewed for both the posts and an applicant can be selected for only one of the posts, what is the number of ways in which the company can select its Director and President from the interviewed applicants?

A. 20
B. 23
C. 25
D. 27
E. 35
Intern
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WE: Programming (Computer Software)
Re: A company interviewed 5 applicants each for the posts of the Director  [#permalink]

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New post 14 Apr 2019, 11:27
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My Understanding is as such :-
Applicants for D - 3 +2 (Jack and Jill)
Applicants for P - 3 +2 (Jack and Jill)

If Jack/Jill is not selected as D, then D has 3 choices, and P has 5 choices.
Therefore, no. of choices = 3*5

If Jack/Jill is selected as D, P has 4 choices.
Therefore no. of choices = 2*4

So, total number of ways for selection = 3 *5 + 2*4 = 15+8 = 23

Let me know if this seems correct
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Re: A company interviewed 5 applicants each for the posts of the Director  [#permalink]

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New post 15 Apr 2019, 19:21
If Jack/Jill is not selected as D, then D has 3 choices, and P has 5 choices.
Therefore, no. of choices = 3*5

But is this not possible in 2 different ways? Like, if Jack/Jill is selected as D, then we have 3*5 choices. But the other way - if Jack/Jill is selected as P, we again have 3*5 choices. Right??
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Re: A company interviewed 5 applicants each for the posts of the Director  [#permalink]

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New post 26 Apr 2019, 08:28
1
I used a different way.

Let's imagine there are 5 different people. Then number of ways is 5*5=25

But Jack and jill cant be elected for both positions. Number of ways to do this is 2.

25-2 =23
Now we need to subtract 2 cases where

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Re: A company interviewed 5 applicants each for the posts of the Director  [#permalink]

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New post 26 Apr 2019, 10:00
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kiran120680 wrote:
A company interviewed 5 applicants each for the posts of the Director and the President. If Jack and Jill were the only applicants who were interviewed for both the posts and an applicant can be selected for only one of the posts, what is the number of ways in which the company can select its Director and President from the interviewed applicants?

A. 20
B. 23
C. 25
D. 27
E. 35


Simplification of the question can be .... There are 2 common candidates in different sets. So unique candidates in each group are 3

D P
3 * 3 = 9
Jack *3 = 3
Jill *3 = 3
3 * Jack = 3
3 * Jill = 3
Jack * Jill = 1
Jill * Jack =1

Total=23

Hope ...I'm correct!...
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Re: A company interviewed 5 applicants each for the posts of the Director   [#permalink] 26 Apr 2019, 10:00
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