Question

How many different ID cards can be made if there are four digits can be used more than once? What if digits can be repeated?

Answer 1

ANSWERS

1) 5,040

2) 10,000

Step-by-step explanation

1) If we have 10 numbers (from 0 to 9), the ID cards have 4 of them and the digits do not repeat, we have 10 numbers to choose from for the first digit, 9 numbers for the second digit, 8 numbers for the third digit, and 7 numbers for the fourth digit. So,

`10\cdot9\cdot8\cdot7=5,040`

Hence, there are 5,040 different ID cards that can be made if no digit can be used more than once.

2) In this case, the numbers can be repeated, so for each of the four digits we have 10 options to choose from,

`10\cdot10\cdot10\cdot10=10^4=10,000`

Hence, there are 10,000 different ID cards that can be made if digits can be repeated.