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# The first name and the last name of 5 people are written in two tables

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Math Expert
Joined: 02 Sep 2009
Posts: 65807
The first name and the last name of 5 people are written in two tables  [#permalink]

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02 Jun 2020, 07:48
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75% (hard)

Question Stats:

21% (02:21) correct 79% (02:27) wrong based on 33 sessions

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The first name and the last name of 5 people are written in two tables above, in a jumbled order. For example, the last name of John may be Garth. Lisa, who doesn’t know the correct first name-last name pair for any of the 5 people in the table, is asked to create 5 first name – last name pairs using each first name and last name in the tables above only once. What is the probability that the pairs she creates includes the correct first name-last name pairs of 2 people in the table?

A. 1/120
B. 1/360
C. 1/240
D. 1/60
E. 1/6

Attachment:

1.png [ 13.96 KiB | Viewed 585 times ]

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Posts: 311
Re: The first name and the last name of 5 people are written in two tables  [#permalink]

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02 Jun 2020, 21:37
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Cheers,
NJ
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10785
Location: Pune, India
The first name and the last name of 5 people are written in two tables  [#permalink]

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05 Jun 2020, 04:21
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Bunuel wrote:

The first name and the last name of 5 people are written in two tables above, in a jumbled order. For example, the last name of John may be Garth. Lisa, who doesn’t know the correct first name-last name pair for any of the 5 people in the table, is asked to create 5 first name – last name pairs using each first name and last name in the tables above only once. What is the probability that the pairs she creates includes the correct first name-last name pairs of 2 people in the table?

A. 1/120
B. 1/360
C. 1/240
D. 1/60
E. 1/6

Attachment:
1.png

The total number of ways in which we can make first name-lastname pairs is 5! = 120 (There are 5 spots and 5 last names)

Out of these 120, there is one arrangement in which all pairs are correct. There are some arrangements in which no pair is correct, in some only 1 pair is correct, some in which 2 pairs are correct and some in which 3 are correct.

We need those arrangements in which 2 pairs are correct. Pick 2 last names in 5C2 ways and put them in their correct place.
Now we have 3 last names to be put in 3 spots. Say Jordan Johnson and Sam Jones are correctly paired.
We are left with Smith, McGill and Garth.
To put next to John, we have 2 options (excluding his actual last name). Say we put Garth.
Now we have 2 last names which can be arranged in only 1 way between the two firstnames so that both are incorrectly placed.
Number of ways of having exactly 2 correct pairs = 5C2*2 = 20 ways

Probability = 20/120 = 1/6

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Karishma
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Joined: 29 Feb 2020
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The first name and the last name of 5 people are written in two tables  [#permalink]

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05 Jun 2020, 04:46
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Bunuel wrote:
The first name and the last name of 5 people are written in two tables above, in a jumbled order. For example, the last name of John may be Garth. Lisa, who doesn’t know the correct first name-last name pair for any of the 5 people in the table, is asked to create 5 first name – last name pairs using each first name and last name in the tables above only once. What is the probability that the pairs she creates includes the correct first name-last name pairs of 2 people in the table?

A. 1/120
B. 1/360
C. 1/240
D. 1/60
E. 1/6

Attachment:
1.png

The total number of ways in which we can make first name-lastname pairs is 5! = 120 (There are 5 spots and 5 last names)

Out of these 120, there is one arrangement in which all pairs are correct. There are some arrangements in which no pair is correct, in some only 1 pair is correct, some in which 2 pairs are correct and some in which 3 are correct.

We need those arrangements in which 2 pairs are correct. Pick 2 last names in 5C2 ways and put them in their correct place.
Now we have 3 last names to be put in 3 spots. Say Jordan Johnson and Sam Jones are correctly paired.
We are left with Smith, McGill and Garth.
To put next to John, we have 2 options (excluding his actual last name). Say we put Garth.
Now we have 2 last names which can be arranged in only 1 way between the two firstnames so that both are incorrectly placed.
Number of ways of having exactly 2 correct pairs = 5C2*2 = 20 ways

Probability = 20/120 = 1/6

Hi Karishma,

thanks so much for the explanation, but I'm sorry I got lost right at the beginning.

Do you mean that the total number of ways to arrange 5 names Lisa has created is 5!? To me, there are only 25 ways you can make names out of the two columns - 5x5 possible name combinations.

Secondly, why are we concerned with number of ways the 5 combo Lisa came up with can be arranged, instead of the possible names available? Shouldn't the possibility of her getting one right name be 5/25 or 1/5? the second one would be 4/24. Of course then we'd have to figure out the variations of placement of the correct names.

Thanks!
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Re: The first name and the last name of 5 people are written in two tables  [#permalink]

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02 Jun 2020, 08:13
for 5 people getting exactly correct their surnames ; 1/5! ; 1/120
and for 2 people ; 5*4 ; 20 ways
so P ; 20/120 ; 1/6
OPTION E

Bunuel wrote:

The first name and the last name of 5 people are written in two tables above, in a jumbled order. For example, the last name of John may be Garth. Lisa, who doesn’t know the correct first name-last name pair for any of the 5 people in the table, is asked to create 5 first name – last name pairs using each first name and last name in the tables above only once. What is the probability that the pairs she creates includes the correct first name-last name pairs of 2 people in the table?

A. 1/120
B. 1/360
C. 1/240
D. 1/60
E. 1/6

Attachment:
1.png
Intern
Joined: 29 Feb 2020
Posts: 4
Re: The first name and the last name of 5 people are written in two tables  [#permalink]

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03 Jun 2020, 21:06
doesn't make sense. someone help please?
Senior Manager
Joined: 14 Aug 2019
Posts: 322
Location: India
Concentration: Marketing, Finance
Re: The first name and the last name of 5 people are written in two tables  [#permalink]

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05 Jun 2020, 04:57
Total number of pairs possibe
5*4*3*2*1= 120

Only 2 correct:
1*1*2*1*1
correct*correct * wrong* wrong*wrong

now these 2 correct can be of any 5 people , so 5 c2= 10 ways

so total probability of choosing any 2 correct pairs = 10*2/120 = 1/6

Re: The first name and the last name of 5 people are written in two tables   [#permalink] 05 Jun 2020, 04:57