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03 Apr 2017, 00:30
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E
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72% (01:03) correct
28%
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In an auditorium, there are ten light switches each of which control the lights of a different zone of the room. If there are only these 10 zones in the room and each light may only be set to "on" or "off", then how many different lighting arrangements are possible in the auditorium?
A. 10^10
B. 10!
C. 10^2
D 5!
E. 2^10
A. 10^10
B. 10!
C. 10^2
D 5!
E. 2^10
avinsethi
Joined: 09 Oct 2016
Last visit: 13 May 2019
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Schools: DeGroote'21 (A) Schulich Sept '21 (A)
03 Apr 2017, 05:23
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10 sets of ligthing, either on/off - 2 options only ... Hence
10 * 2C1 = 2^10 (E)
10 * 2C1 = 2^10 (E)
03 Apr 2017, 08:06
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Bunuel
Let the 10 light switches be Switch #1, Switch #2, Switch #3, etc.
Take the task of creating a lighting arrangement and break it into stages.
Stage 1: Set Switch #1
The switch can be ON or OFF. So, we can complete stage 1 in 2 ways
Stage 2: Set Switch #2
The switch can be ON or OFF. So, we can complete stage 2 in 2 ways
Stage 3: Set Switch #3
The switch can be ON or OFF. So, we can complete stage 3 in 2 ways
Stage 4: Set Switch #4
The switch can be ON or OFF. So, we can complete stage 4 in 2 ways
.
.
.
Stage 9: Set Switch #9
The switch can be ON or OFF. So, we can complete stage 9 in 2 ways
Stage 10: Set Switch #10
The switch can be ON or OFF. So, we can complete stage 10 in 2 ways
By the Fundamental Counting Principle (FCP), we can complete all 10 stages (and thus create a lighting arrangement) in (2)(2)(2)(2)(2)(2)(2)(2)(2)(2) ways (= \(2^{10}\) ways)
Answer:
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn the technique.
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