Question

A home alarm system randomly assigns a five-character code for each customer. The code will not repeat a character. The characters are 1, 2, 3, 4, 5, E, M, T, G, Y, and R. What is the total number of codes that can be randomly assigned?

A.) 1,320
B.) 95,040
C.) 9,540
D.) 11,880

Answer 1

The total number of codes which can be assigned is, 55440 .

Explanation:

According to the question, the home alarm system randomly assigns a five-character code for each customer.The code will not repeat a character and there are 11 distinct characters.

So, the total number of codes that can be randomly assigned is given by,

`^(11){P}_(5)`

=
`\frac {11!}{6!}`

=
`11 * 10 * 9 * 8 * 7`

= 55440