VyshakhR1995
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
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:
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
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