GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 26 Jun 2019, 03:22

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

In How many ways can 7 people park cars in slots allotted to them?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Manager
Manager
avatar
G
Joined: 12 Jun 2016
Posts: 212
Location: India
Concentration: Technology, Leadership
WE: Sales (Telecommunications)
GMAT ToolKit User
In How many ways can 7 people park cars in slots allotted to them?  [#permalink]

Show Tags

New post 02 Jul 2016, 03:22
1
9
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

52% (01:30) correct 48% (01:45) wrong based on 209 sessions

HideShow timer Statistics


Seven friends are living in 7 different flats of an apartment. Each of them was allotted a parking slot to park their cars in the ground floor. But they used to park their cars randomly in any of the seven slots. In how many ways can they park their cars so that exactly five persons park their cars in the slots allotted to them?

A) 14
B) 21
c) 35
D) 42
E) 49

_________________
My Best is yet to come!
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55802
Re: In How many ways can 7 people park cars in slots allotted to them?  [#permalink]

Show Tags

New post 02 Jul 2016, 04:51
5
susheelh wrote:
Seven friends are living in 7 different flats of an apartment. Each of them was allotted a parking slot to park their cars in the ground floor. But they used to park their cars randomly in any of the seven slots. In how many ways can they park their cars so that exactly five persons park their cars in the slots allotted to them?

A) 14
B) 21
c) 35
D) 42
E) 49


\(C^5_7=21\): choosing which of the 7 persons will be on the slots allocates to them, the remaining 2 will be parked on each others slots.

Answer: B.
_________________
General Discussion
Intern
Intern
avatar
B
Joined: 18 Oct 2018
Posts: 4
Location: United States (TX)
GMAT 1: 640 Q48 V30
GPA: 3.89
Re: In How many ways can 7 people park cars in slots allotted to them?  [#permalink]

Show Tags

New post 25 Nov 2018, 21:44
I did not understand how answer is 21.
I calculated as:-
1x1x1x1x1x2C1x1x2!x3!=24
isnt this right? and why?
Intern
Intern
avatar
B
Joined: 16 Oct 2018
Posts: 8
Re: In How many ways can 7 people park cars in slots allotted to them?  [#permalink]

Show Tags

New post 28 Nov 2018, 21:27
Why do we use the combination formula instead of the permutation formula?
Manager
Manager
avatar
D
Joined: 17 May 2015
Posts: 248
Re: In How many ways can 7 people park cars in slots allotted to them?  [#permalink]

Show Tags

New post 28 Nov 2018, 23:28
1
Zynxu wrote:
Why do we use the combination formula instead of the permutation formula?


Hi Zynxu,
Question asks:

In how many ways can they park their cars so that exactly five persons park their cars in the slots allotted to them?

Or in other words, we can say in how many ways two parks will be parked in the wrong slot?

For example. car no. 6 and car no. 7 are parked in the wrong slot. This we won't count as 2, rather we will count as 1 way only.
Hence you need to apply combination.

Another way we can think as follows:

Suppose car no. 1 in in the wrong place, so all possible combination for the car no. 1 will be:

(1,2), (1,3), (1,4), (1,5), (1,6), (1,7) --- Total 6 ways.

For car no. 2, the following possibilities are there:

(2,1), (2,3), (2,4), (2,5) (2,6), (2,7) --- Total 6 ways.

Similarly, for all other cars, we'll have 6 such possibilities.

Hence the total number of ways = 7*6 = 42 ways.

But, we are double counting each option. Hence, we need to divide the final answer by 2.

The required number of ways = 42/2 = 21 ways.

Hope this helps.

Thanks.
Intern
Intern
avatar
B
Joined: 08 Jan 2018
Posts: 20
Location: India
Concentration: Operations, General Management
WE: Project Management (Manufacturing)
Re: In How many ways can 7 people park cars in slots allotted to them?  [#permalink]

Show Tags

New post 29 Nov 2018, 02:44
1
Pick any 5 person from 7 person = 5C7 = 7*6/3= 21 ways
These people parked on their respective slots.

Remaining 2 people & 2 Slots. only one way to park (i.e on other's parking space) possible. =1 way
Total possible ways= 21*1=21

Ans.B
Intern
Intern
avatar
B
Joined: 05 Oct 2018
Posts: 43
Location: United States
GMAT 1: 770 Q49 V47
GPA: 3.95
WE: General Management (Other)
Re: In How many ways can 7 people park cars in slots allotted to them?  [#permalink]

Show Tags

New post 29 Nov 2018, 13:57
aditishah02 wrote:
I did not understand how answer is 21.
I calculated as:-
1x1x1x1x1x2C1x1x2!x3!=24
isnt this right? and why?



Can you provide more information on your logic/intent behind that calculation?
Intern
Intern
avatar
Joined: 15 Oct 2018
Posts: 1
Re: In How many ways can 7 people park cars in slots allotted to them?  [#permalink]

Show Tags

New post 29 Nov 2018, 19:02
7!/(7-5)!5!
This will give 21

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 10 Nov 2018
Posts: 33
Location: France
GMAT 1: 600 Q48 V25
GMAT 2: 680 Q49 V34
GRE 1: Q163 V161
GPA: 3.6
Re: In How many ways can 7 people park cars in slots allotted to them?  [#permalink]

Show Tags

New post 30 Nov 2018, 10:38
Bunuel wrote:
susheelh wrote:
Seven friends are living in 7 different flats of an apartment. Each of them was allotted a parking slot to park their cars in the ground floor. But they used to park their cars randomly in any of the seven slots. In how many ways can they park their cars so that exactly five persons park their cars in the slots allotted to them?

A) 14
B) 21
c) 35
D) 42
E) 49


\(C^5_7=21\): choosing which of the 7 persons will be on the slots allocates to them, the remaining 2 will be parked on each others slots.

Answer: B.


Super. I did the 7C5 but then i multiplied it by 2 thinking that the remaining cars can be parked in two ways whereas there is only one arrangement for them, as the last one would mean that they are in their correct places, which does not fit the answer. (a very confusing statement!!!)
Intern
Intern
avatar
Joined: 24 Aug 2017
Posts: 1
Re: In How many ways can 7 people park cars in slots allotted to them?  [#permalink]

Show Tags

New post 30 Nov 2018, 18:58
MayankSingh wrote:
Pick any 5 person from 7 person = 5C7 = 7*6/3= 21 ways
These people parked on their respective slots.

Remaining 2 people & 2 Slots. only one way to park (i.e on other's parking space) possible. =1 way
Total possible ways= 21*1=21

Ans.B

shouldn't it be 7C5????? and 42/2.... not 42/3......


☺☺

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 13 Jul 2018
Posts: 2
In How many ways can 7 people park cars in slots allotted to them?  [#permalink]

Show Tags

New post 05 Dec 2018, 11:03
What I simply did was added the pairs of remaining 2 people who will have to park in each others spots:
Such as: 12,13,14,15,16,17,
23,24,25,26,27,
34,35,36,27,
45,46,47,
56,57,
67.

Hence option B. 21.
Notice that 12 is the same as 21, 23 is the same as 32, and so on. Hence, those need to be ignored.
Hope this helps :)
GMAT Club Bot
In How many ways can 7 people park cars in slots allotted to them?   [#permalink] 05 Dec 2018, 11:03
Display posts from previous: Sort by

In How many ways can 7 people park cars in slots allotted to them?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne