Question

"how many ways are there to construct a string of 3 digits if numbers cannot be repeated

Answer 1

`\underbrace{10}_{\text{1 of 10 digits}}\cdot \underbrace{9}_{\text{1 of remaining 9 digits}}\cdot \underbrace{8}_{\text{1 of remaining 8 digits}}=720`

Answer 2

there are 10 total digits ( 0, 1 , 2, 3, 4, 5, 6, 7,8 ,9)

1st digit can be 1 of 10
2nd digit can be 1 of 9 ( 10-1 because a number cannot repeat)
3rd digit can be 1 of 8 ( 9-1 because no number can repeat)

total combinations = 10 * 9 * 8 = 720