It is currently 21 Jul 2019, 09:25

### 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

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

# There are 5 doors to a lecture room. Two are red and the oth

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 7401
Followers: 125

Kudos [?]: 1450 [0], given: 6611

There are 5 doors to a lecture room. Two are red and the oth [#permalink]  08 May 2019, 04:26
Expert's post
00:00

Question Stats:

50% (01:16) correct 50% (00:00) wrong based on 2 sessions
There are 5 doors to a lecture room. Two are red and the others are green. In how many ways can a lecturer enter the room and leave the room from different colored doors?

(A) 1

(B) 3

(C) 6

(D) 9

(E) 12
[Reveal] Spoiler: OA

_________________
Manager
Joined: 03 Apr 2019
Posts: 69
Followers: 0

Kudos [?]: 38 [1] , given: 1

Re: There are 5 doors to a lecture room. Two are red and the oth [#permalink]  12 May 2019, 20:23
1
KUDOS
We can see that 2 red doors are identical and 3 green doors are identical. R=2 and G=3
Now the combination part comes as if we enter red door first - selecting one door to enter (red) from two possible doors and then selecting one door to exit( green) from three possible green doors - 2C1*3C1 will be case 1
If we enter from the Green door - selecting one door to enter (Green) from possible doors (Green) then selecting one door to exit (red) from two possible doors( Red) - 3C1*2C1 will be case 2
Total makes : 2C1*3C1+3C1*2C1 = 6+6= 12
MyGuru Representative
Affiliations: Partner at MyGuru LLC.
Joined: 13 May 2019
Posts: 117
Location: United States
GMAT 1: 770 Q51 V44
GRE 1: Q169 V168
WE: Education (Education)
Followers: 1

Kudos [?]: 103 [1] , given: 2

Re: There are 5 doors to a lecture room. Two are red and the oth [#permalink]  13 May 2019, 07:26
1
KUDOS
Expert's post
To avoid using Combination or Permutation notation, you can always just consider the following steps to manually calculate the scenario:

1) Draw a ____ for Each Selection to be Made and Label any Dictated Restrictions for the Selection.
In this Case there will be a selection of two doors:
Door 1 and Door 2

2) Determine Most Efficient Method to Properly and Specifically Make Selection based on Problem and Consider Whether Selecting this or That.
In this Case the First door Selection Impacts the Second Door Selection So We Need to Split into Two Scenarios:
Door 1 (Red) and Door 2 (Green)
OR
Door 1 (Green) and Door 2 (Red)

3) Then Insert the Number or Available Options to Select at Moment of Selection One Blank at a Time
In this Case for the first iteration:
2 options (Red) and 3 options (Green)
OR
3 options (Green) and 2 options (Red)

4) Finally, calculate. When Selecting This AND That - Multiply. So, in the first iteration there are 2 x 3 = 6 ways to enter a Red door and exit a Green door as well as 3 x 2 = 6 ways to enter a Green door and exit a Red door in the second iteration. Then, when it is possible to Select this OR That - Add. So, add the 6 ways to proceed Red then Green to the 6 ways to proceed Green then Red to determine that there are 12 total ways to enter one color door and exit the other.
_________________

Stefan Maisnier

GRE Instructor
Joined: 10 Apr 2015
Posts: 2175
Followers: 64

Kudos [?]: 1986 [1] , given: 20

Re: There are 5 doors to a lecture room. Two are red and the oth [#permalink]  13 May 2019, 09:09
1
KUDOS
Expert's post
Carcass wrote:
There are 5 doors to a lecture room. Two are red and the others are green. In how many ways can a lecturer enter the room and leave the room from different colored doors?

(A) 1

(B) 3

(C) 6

(D) 9

(E) 12

Since all the answer choices are small, we could also just list and count the possible outcomes

Let A and B be the 2 RED doors
Let C, D and E be the 3 GREEN doors

So, the possible outcomes are:
ENTER through door A, and EXIT through door C
ENTER through door A, and EXIT through door D
ENTER through door A, and EXIT through door E

ENTER through door B, and EXIT through door C
ENTER through door B, and EXIT through door D
ENTER through door B, and EXIT through door E

ENTER through door C, and EXIT through door A
ENTER through door C, and EXIT through door B

ENTER through door D, and EXIT through door A
ENTER through door D, and EXIT through door B

ENTER through door E, and EXIT through door A
ENTER through door E, and EXIT through door B

There are 12 possible outcomes.

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: There are 5 doors to a lecture room. Two are red and the oth   [#permalink] 13 May 2019, 09:09
Display posts from previous: Sort by