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Will must choose a 3-character computer password, consisting

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by Jay@ManhattanReview » Mon Nov 04, 2019 10:29 pm
ktrout2020 wrote: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

Source: Princeton Review
Number of ways the 3 characters can be arranged to form passwords = 3! = 6

Number of ways 2 districts digits can be chosen out of 10 digits = 10C2 = 10.9 / 1.2 = 45

Number of ways 1 letter can be chosen out of 26 letters = 26

Thus, the number of different passwords Will can choose = 6*45*26 = 7,020.

The correct answer: D

Hope this helps!

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by Brent@GMATPrepNow » Tue Nov 05, 2019 6:01 am
ktrout2020 wrote: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

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:

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MEDIUM
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- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
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DIFFICULT
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- https://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by [email protected] » Tue Nov 05, 2019 11:18 am
Hi All,

We're told that Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order. We're asked for the total number of different passwords that Will can choose. Depending on how comfortable you are with the 'math' involved, you can perform the calculations in a couple of different ways. Here's how you can break the prompt down into smaller pieces (which you might find easier than trying to do one gigantic calculation).

Based on the the 'restrictions' in the prompt, we can use 1 letter of the English alphabet and 2 DISTINCT digits IN ANY ORDER to make a code. Thus, the code could be one of 3 options:

(Letter)(Digit)(Different Digit)
(Digit)(Letter)(Different Digit)
(Digit)(Different Digit)(Letter)

The first option = (Letter)(Digit)(Different Digit) = (26)(10)(9) = 2340
The second option = (Digit)(Letter)(Different Digit) = (10)(26)(9) = 2340
The third option = (Digit)(Different Digit)(Letter) = (10)(9)(26) = 2340

You might recognize that each calculation involves the product of the same 3 numbers, so you don't have to do that calculation each time - just do it once and then multiply that result by 3....

Total options = 3(2340) = 7020 options

Final Answer: [spoiler=]D[/spoiler]

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by Scott@TargetTestPrep » Wed Nov 06, 2019 7:15 pm
ktrout2020 wrote: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

Source: Princeton Review
Since there are 26 letters and 10 digits, the number of 3-character passwords that can be created is 26 x 10 x 9 = 2,340, if the password is in the form of LDD where L means letter and D means digit. However, the password can be also in the form of DLD and DDL, each of which also can be created in 2,340 ways. Thus, the total number of passwords is 2,340 x 3 = 7,020.

Answer: D

Scott Woodbury-Stewart
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by Scott@TargetTestPrep » Mon Nov 11, 2019 1:19 pm
ktrout2020 wrote: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

Source: Princeton Review
Since there are 26 letters and 10 digits, the number of 3-character passwords that can be created is 26 x 10 x 9 = 2,340, if the password is in the form of LDD, where L means letter and D means digit. However, the password can also be in the form of DLD and DDL, each of which can also be created in 2,340 ways. Thus, the total number of passwords is 2,340 x 3 = 7,020.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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