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? Answers.
A) fewer than 1,000  B) between 1,000 and 10,000  C) between 10,000 and 100,000  D) between 100,000 and 1,000,000  E) more than 1,000,000
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 between 10,000 and 100,000)between 10,000 and 100,000
<result>C</result>
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?