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

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,

[tex]^{11}{P}_{5}[/tex]

= [tex]\frac {11!}{6!}[/tex]

= [tex]11 \times 10 \times 9 \times 8 \times 7[/tex]

= 55440

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

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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