When she chooses a password, Eloise
When she chooses a password, Eloise
always uses exactly ten different
characters: five letters (A, B, C, D, and E)
and five numbers (2, 3, 4, 5, and 6).
Additionally, she always ensures that no
pair of letters is consecutive and that no
pair of numbers is consecutive. How many
different passwords conform to these rules?
Answer/Solution
between 10,000 and 100,000
Steps/Work
The first character of the password can be any letter or number, so Eloise has ten
options. Her second choice must be from the set (letter or number) not yet used, so she
has five options. Choice 3 is from the same set as Choice 1, and she has four options left.
Choice 4 is the second item from the same set as Choice 2, so she has four options.
Choices 5 and 6 are from different sets, each with three options; Choices 7 and 8 are from
different sets, each with two options; Choices 9 and 10 are from different sets, each with
only one option remaining. You can see this information in the following chart:
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
10 5 4 4 3 3 2 2 1 1
To find the total number of possible passwords, multiply these numbers together:
10 × 5 × 4 × 4 × 3 × 3 × 2 × 2 × 1 × 1 = 28,800
correct anser C)between 10,000 and 100,000
options. Her second choice must be from the set (letter or number) not yet used, so she
has five options. Choice 3 is from the same set as Choice 1, and she has four options left.
Choice 4 is the second item from the same set as Choice 2, so she has four options.
Choices 5 and 6 are from different sets, each with three options; Choices 7 and 8 are from
different sets, each with two options; Choices 9 and 10 are from different sets, each with
only one option remaining. You can see this information in the following chart:
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
10 5 4 4 3 3 2 2 1 1
To find the total number of possible passwords, multiply these numbers together:
10 × 5 × 4 × 4 × 3 × 3 × 2 × 2 × 1 × 1 = 28,800
correct anser C)between 10,000 and 100,000