Question

PLEASE HELP! A new school randomly assigns a six character student code to every prospective student. The school uses the characters 1, 2, 3, 4, 5, X, Y, and Z. If none of the student codes contain a repeated character, what is the total number of codes that can be randomly assigned?

Answer 1

Answer: 20160

Step-by-step explanation:

Here, the total number of character = 8 ( 1, 2, 3, 4, 5, X, Y, Z)

Since, we have to form a code by any 6 character from these character.

If there are no repeated character in any code.

Then, In the code,

The total possible outcomes of first digit  = 8

The total possible outcomes of second digit = 7

The total possible outcomes of third digit = 6

The total possible outcomes of fourth digit  = 5

The total possible outcomes of fifth digit = 4

The total possible outcomes of sixth digit  = 3

Therefore, the total possible codes = 8 × 7 × 6 × 5 × 4 × 3 = 20160