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.
A man 8 friends whom he wants to invite for dinner. The number of ways
[#permalink]
04 Oct 2021, 04:45
04 Oct 2021, 04:45
Expert Reply
2
Bookmarks
00:00
Question Stats:
42% (02:28) correct
57% (01:01) wrong based on 21 sessions
Hide Show timer Statistics
A man has 8 friends whom he wants to invite for dinner. The number of ways in which he can invite at least one of them is
A)8
B)255
C)8!-1
D)256
E)7
A)8
B)255
C)8!-1
D)256
E)7
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
A man 8 friends whom he wants to invite for dinner. The number of ways
[#permalink]
04 Oct 2021, 05:32
04 Oct 2021, 05:32
Carcass wrote:
A man has 8 friends whom he wants to invite for dinner. The number of ways in which he can invite at least one of them is
A)8
B)255
C)8!-1
D)256
E)7
A)8
B)255
C)8!-1
D)256
E)7
Take the task of inviting friends and break it into stages.
ASIDE: Let's let A, B, C, D, E, F, G and H represent the 8 friends
Stage 1: Decide whether or not to invite friend A
You have 2 options: invite friend A or don't invite friend A
So, we can complete stage 1 in 2 ways
Stage 2: Decide whether or not to invite friend B
You have 2 options: invite friend B or don't invite friend B
So, we can complete stage 2 in 2 ways
Stage 3: Decide whether or not to invite friend C
So, we can complete stage 3 in 2 ways
.
.
.
Stage 8: Decide whether or not to invite friend H
So, we can complete stage 8 in 2 ways
By the Fundamental Counting Principle (FCP), we can complete all 8 stages (and create a guest list) in (2)(2)(2)(2)(2)(2)(2)(2) ways (= 256 ways)
NOTE: in these calculations, one of the possible outcomes is that ZERO friends are invited. The question says that AT LEAST ONE friend must come.
So, we must subtract this 1 outcome from our solution.
So, total number of ways to invite friends = 256 - 1 = 255
Answer: B
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: A man 8 friends whom he wants to invite for dinner. The number of ways
[#permalink]
08 May 2022, 21:44
08 May 2022, 21:44
GreenlightTestPrep wrote:
Carcass wrote:
A man 8 friends whom he wants to invite for dinner. The number of ways in which he can invite at least one of them is
A)8
B)255
C)8!-1
D)256
E)7
A)8
B)255
C)8!-1
D)256
E)7
Take the task of inviting friends and break it into stages.
ASIDE: Let's let A, B, C, D, E, F, G and H represent the 8 friends
Stage 1: Decide whether or not to invite friend A
You have 2 options: invite friend A or don't invite friend A
So, we can complete stage 1 in 2 ways
Stage 2: Decide whether or not to invite friend B
You have 2 options: invite friend B or don't invite friend B
So, we can complete stage 2 in 2 ways
Stage 3: Decide whether or not to invite friend C
So, we can complete stage 3 in 2 ways
.
.
.
Stage 8: Decide whether or not to invite friend H
So, we can complete stage 8 in 2 ways
By the Fundamental Counting Principle (FCP), we can complete all 8 stages (and create a guest list) in (2)(2)(2)(2)(2)(2)(2)(2) ways (= 256 ways)
NOTE: in these calculations, one of the possible outcomes is that ZERO friends are invited. The question says that AT LEAST ONE friend must come.
So, we must subtract this 1 outcome from our solution.
So, total number of ways to invite friends = 256 - 1 = 255
Answer: B
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
RELATED VIDEO
Hi Brent,
NOTE: in these calculations, one of the possible outcomes is that ZERO friends are invited. The question says that AT LEAST ONE friend must come.
So, we must subtract this 1 outcome from our solution.
So, total number of ways to invite friends = 256 - 1 = 255
Does this mean - he sends out 256 invites with two options - Attending / Not attending.
If thats the case if he wants atleast one friend to come -why cant the answer be 2^7 * 1
Can you please kindly comment.
Thanks in advance.
