GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
There are 5 couples. If they will sit 10 chairs in a row such that eac
[#permalink]
06 Oct 2021, 09:14
06 Oct 2021, 09:14
Expert Reply
3
Bookmarks
00:00
Question Stats:
47% (01:34) correct
52% (01:23) wrong based on 23 sessions
Hide Show timer Statistics
There are 5 couples. If they will sit 10 chairs in a row such that each couple sits side by side, how many possible cases are there?
A. 120
B. 240
C. 1,200
D. 2,460
E. 3,840
A. 120
B. 240
C. 1,200
D. 2,460
E. 3,840
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
There are 5 couples. If they will sit 10 chairs in a row such that eac
[#permalink]
06 Oct 2021, 09:26
06 Oct 2021, 09:26
2
Carcass wrote:
There are 5 couples. If they will sit 10 chairs in a row such that each couple sits side by side, how many possible cases are there?
A. 120
B. 240
C. 1,200
D. 2,460
E. 3,840
A. 120
B. 240
C. 1,200
D. 2,460
E. 3,840
Here's one approach:
Take the task of seating the 10 people and break it into stages.
Stage 1: Select someone to sit in the 1st chair
There are 10 people to choose from, so we can complete stage 1 in 10 ways
Stage 2: Select someone to sit in the 2nd chair
The person seated in the 2nd chair must be the partner of the person in the 1st chair
So we can complete this stage in 1 way.
Stage 3: Select someone to sit in the 3rd chair
There are 8 people remaining. So, we can complete stage 3 in 8 ways
Stage 4: Select someone to sit in the 4th chair
The person seated in the 4th chair must be the partner of the person in the 3rd chair
So, we can complete this stage in 1 way.
Stage 5: Select someone to sit in the 5th chair
There are 6 people remaining. So, we can complete stage 5 in 6 ways
Stage 6: Select someone to sit in the 6th chair
The person seated in the 6th chair must be the partner of the person in the 5th chair
So, we can complete this stage in 1 way.
Stage 7: Select someone to sit in the 7th chair
There are 4 people remaining. So, we can complete stage 7 in 4 ways
Stage 8: Select someone to sit in the 8th chair
The person seated in the 8th chair must be the partner of the person in the 7th chair
So, we can complete this stage in 1 way.
Stage 9: Select someone to sit in the 9th chair
There are 2 people remaining. So, we can complete stage 9 in 2 ways
Stage 10: Select someone to sit in the 10th chair
One 1 person remains.
So, we can complete this stage in 1 way.
By the Fundamental Counting Principle (FCP), we can complete all 10 stages (and thus seat all 10 people) in (10)(1)(8)(1)(6)(1)(4)(1)(2)(1) ways (= 3840 ways)
Answer: E
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE, so be sure to learn it.
RELATED VIDEO
Re: There are 5 couples. If they will sit 10 chairs in a row such that eac
[#permalink]
06 Oct 2021, 14:07
06 Oct 2021, 14:07
2
10 people means 5 couple.
5 couple can be arranged in 5*4*3*2*1=120 ways another couple means two people and they can sit as H,W or W,H =2*1
for 5 couple =2*2*2*2*2=32
total number of ways it can be arranged=120*32=3840.
5 couple can be arranged in 5*4*3*2*1=120 ways another couple means two people and they can sit as H,W or W,H =2*1
for 5 couple =2*2*2*2*2=32
total number of ways it can be arranged=120*32=3840.
