Brent@GMATPrepNow wrote:RBBmba@2014 wrote:In a test of 8 questions, each question has an alternative.What is the number of ways in which one can select one or more questions ?
(A) 2^8-1
(B) 2^8
(C) 2^8*3
(D) 3^8-1
(E) 3^8
Take the task of selecting or not selecting questions and break it into
stages.
Stage 1: Select or don't select question #1
We have 2 options: select the question or don't select the question.
So, we can complete stage 1 in
2 ways
Stage 2: Select or don't select question #2
We have 2 options: select the question or don't select the question.
So, we can complete stage 2 in
2 ways
Stage 3: Select or don't select question #3
We have 2 options: select the question or don't select the question.
So, we can complete stage 3 in
2 ways
.
.
.
.
Stage 8: Select or don't select question #8
We have 2 options: select the question or don't select the question.
So, we can complete stage 8 in
2 ways
By the Fundamental Counting Principle (FCP), we can complete all 8 stages (and thus deal with all 8 questions) in
(2)(2)(2)(2)(2)(2)(2)(2) ways (= 2^8 ways)
So, the correct answer is E . . . . NOPE!
Included in those 2^8 ways is a single case in which NONE of the questions are selected. HOWEVER, the question tells us that we must select
one or more questions. So, we should not have counted that 1 case in which NONE of the questions are selected.
So, we must subtract 1 from our answer to get [spoiler]2^8 - 1[/spoiler]
Answer:
D
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Cheers,
Brent
