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A company interviewed 5 applicants each for the posts of the 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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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
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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
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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 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, 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]

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New post 03 Dec 2019, 07:31
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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


Jack = X, Jill = Y

CASES:
X for D and Y for P: 1*1=1
Y for D and X for P: 1*1=1
X for D and ≠Y for P: 1*3C1=3
X for P and ≠Y for D: 1*3C1=3
Y for D and ≠X for P: 1*3C1=3
Y for P and ≠X for D: 1*3C1=3
Not X or Y for any: 3C1*3C1=9

Total: 2+3(4)+9=2+12+9=23

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

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New post 05 Dec 2019, 20:21
1
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


If both Jack and Jill are selected, then there are 2 ways: Jack is the Director and Jill is the President, and vice versa.

If Jack is selected and Jill is not, then there are 1 x 3 = 3 ways if Jack is selected as the Director and another 3 ways if he is selected as the President. Therefore, there are a total of 6 ways if Jack is selected and Jill is not.

Likewise, there are a total of 6 ways if Jill is selected (as either the Director or the President) and Jill is not (selected at all).

Finally, if neither Jack nor Jill is selected, then there are 3 x 3 = 9 ways for the Director and the President to be chosen.

Therefore, there are a total of 2 + 6 + 6 + 9 = 23 ways.

Alternate Solution:

If Jack is selected as the Director, then he cannot be selected as the President, and thus, there are 4 choices (one of which is Jill) for the position of President. Thus, the company can fill the positions in 4 ways when Jack is the Director.

If Jill is selected as the Director, then she cannot be selected as the President, and thus, there are 4 choices (one of which is Jack) for the position of President. Thus, the company can fill the positions in 4 ways where Jill is the Director.

Suppose neither Jack nor Jill is selected for the position of Director. This means that one of the 5 - 2 = 3 candidates is chosen for this position. Further, since neither Jack nor Jill is selected as the Director, there are 5 candidates for the position of President (including Jack and Jill). Thus, there are 3 x 5 = 15 ways the company can fill the positions where neither Jack nor Jill is the Director.

In total, there are 4 + 4 + 15 = 23 ways the company can fill the positions.

Answer: B
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Re: A company interviewed 5 applicants each for the posts of the Director   [#permalink] 05 Dec 2019, 20:21
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