BTGModeratorVI wrote: ↑Sun Feb 23, 2020 6:51 am
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose?
A. 390
B. 2,340
C. 4,680
D. 7,020
E. 14,040
Answer:
D
Source: Princeton Review
Take the task of creating a password and break it into
stages.
Stage 1: Select the one letter to be used in the code
There are 26 letters from which to choose, so we can complete this stage in
26 ways.
Stage 2: Select the two digits to be used in the code
Since the order in which we select the two digits does not matter, we can use combinations.
We can select 2 digits from 10 women in 10C2 ways (45 ways)
So, we can complete stage 2 in
45 ways
NOTE: We now have the 3 characters to be used in the code. At this point, we need to arrange those 3 characters.
Stage 3: Arrange the 3 selected characters.
RULE: We can arrange n unique objects in n! ways.
So, we can arrange the 3 characters in 3! ways (6 ways)
So we can complete stage 3 in
6 ways.
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a password ) in
(26)(45)(6) ways
(26)(45)(6) = 7020
Answer: D
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch this free video:
https://www.gmatprepnow.com/module/gmat- ... /video/775
You can also watch a demonstration of the FCP in action:
https://www.gmatprepnow.com/module/gmat ... /video/776
Then you can try solving the following questions:
EASY
-
https://www.beatthegmat.com/what-should- ... 67256.html
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https://www.beatthegmat.com/counting-pro ... 44302.html
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https://www.beatthegmat.com/picking-a-5- ... 73110.html
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https://www.beatthegmat.com/permutation- ... 57412.html
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https://www.beatthegmat.com/simple-one-t270061.html
MEDIUM
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https://www.beatthegmat.com/combinatoric ... 73194.html
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https://www.beatthegmat.com/arabian-hors ... 50703.html
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https://www.beatthegmat.com/sub-sets-pro ... 73337.html
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https://www.beatthegmat.com/combinatoric ... 73180.html
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https://www.beatthegmat.com/digits-numbers-t270127.html
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https://www.beatthegmat.com/doubt-on-sep ... 71047.html
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https://www.beatthegmat.com/combinatoric ... 67079.html
DIFFICULT
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https://www.beatthegmat.com/wonderful-p- ... 71001.html
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https://www.beatthegmat.com/permutation- ... 73915.html
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https://www.beatthegmat.com/permutation-t122873.html
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https://www.beatthegmat.com/no-two-ladie ... 75661.html
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https://www.beatthegmat.com/combinations-t123249.html
Cheers,
Brent
