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Will must choose a 3-character computer password, consisting of 1 lett
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15 Oct 2021, 04:49
15 Oct 2021, 04:49
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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
A. 390
B. 2,340
C. 4,680
D. 7,020
E. 14,040
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Re: Will must choose a 3-character computer password, consisting of 1 lett
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15 Oct 2021, 05:17
15 Oct 2021, 05:17
3
Carcass 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
A. 390
B. 2,340
C. 4,680
D. 7,020
E. 14,040
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
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Re: Will must choose a 3-character computer password, consisting of 1 lett
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29 Mar 2025, 15:40
29 Mar 2025, 15:40
1
First digit 10 ways
Second digit 9 ways
Third position for letter 26 ways
Since it can be in any order 3C1
10 x 9 x 26 x 3 = 7020
Second digit 9 ways
Third position for letter 26 ways
Since it can be in any order 3C1
10 x 9 x 26 x 3 = 7020
