Question

A certain identification number is a sequence of five digits. (a) How many identification numbers are possible? Incorrect: Your answer is incorrect. numbers (b) How many of them begin with either 023 or 003? numbers (c) How many identification numbers are possible if no two adjacent digits are the same? (For example, 123-45 is permitted, but 123-34 is not.) numbers

Answer 1

100,000

200

65,610

Explanation:

Given that:

Identification number = 5 digits

A.) number of identification numbers possible :

Possible digits : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Total digits possible = 10

Each digit can be any of the 10;

Hence,

10 * 10 * 10 * 10 * 10 = 100,000 possibilities

B.) How many of them begin with either 023 or 003

023 or 003

0 or 0 = 1 option

2 or 0 = 2 options

3 or 3 = 1 option

Other digits will have any of the 10 options :

1 * 2 * 1 * 10 * 10 = 200

3.) if no two digits that follow each other are the same, then only the first digit has 10 options with the other 4 each having 9

10 * 9 * 9 * 9 * 9 = 65,610