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A man 8 friends whom he wants to invite for dinner. The number of ways
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04 Oct 2021, 04:45
04 Oct 2021, 04:45
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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
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A man 8 friends whom he wants to invite for dinner. The number of ways
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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
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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.
