Question

A home alarm system randomly assigns a five-character code for each person. The code will not repeat a character. The characters are 0, 1, 2, 3, 4, 5, M, V, T, G, Y, or R. What is the total number of codes that can be randomly assigned? A. 1,320 codes B. 95,040 codes C. 9,540 codes D. 11,880 codes

Answer 1

Answer:

Option: B is the correct answer.

                        B.  95040 codes

Step-by-step explanation:

There are a total of 12 characters which could be assigned.

The characters are:

       0, 1, 2, 3, 4, 5, M, V, T, G, Y, or R.

We have to make a five-character code.

Also, none of the characters in the code could be repeated.

This means that we have to choose any 5 of the 12 characters and arrange them so as to get  a code.

Hence, total number of such codes possible are given by the formula:

                                   ${12}_P_{5}$

Hence, it is calculated as:

${12}_P_{5}=\dfrac{12!}{(12-5)!}\\\\\\{12}_P_{5}=\dfrac{12!}{7!}\\\\\\{12}_P_{5}=12\times 11\times 10\times 9\times 8=95040$

Answer 2

If you have 12 "digits" selected 5 at a time. The total number of codes available = 12^5 = 248832.