Question

How many 3 digit passcodes are possible if the digits, chosen from the set {1, 2, 3, 4, 5}, cannot be repeated and the first digit must be an even number.

Answer 1

Answer: 24

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Step-by-step explanation:

The first digit must be even, so we have this subset {2,4} to pick from for that first digit. There are 2 choices here.

Whatever is picked for the first digit cannot be re-selected. So we have 5-1 = 4 choices left for the second digit, and then 4-1 = 3 choices for the third digit.

Overall we have 2*4*3 = 24 different passcodes.