decimal digits: how many strings of four digits have....

[hidermann]

I am not sure what steps I should take to solve the following:

5. How many strings of four decimal digits...

(a) have at least one digit that is 9?
(b) have one digit that is 9 and do not contain the same digit twice?

Thank you!

 

[Goistein]

There are 9 coices for the first digit, and 10 for the others. That makes 9*10*10*10=9000. Then subtract all numbers that don't have 9. For part b, do the same thing, but instead of 9*10*10*10, it's 9*9*8*7.

 

[arthur ohlsten]

a)
have at least one digit of 9?

how many combinations of 4 digits are there? 10*10*10*10
10^4

how many combinations of digits are there with no 9's? 9*9*9*9
9^4

how many combinations of 4 digits have at least one 9?
10^4-9^4 answer

b
how many have at least one nine and no duplicats digits?
let the first digit be a nine, the second one of the remaining 9, the next one of the remaing 8, and the last one of the remaing 7; Or the first one of 9 the second be a nine the third one of the remaining 8, and the last one of the remaining 7;Or.[the same argument for the third and fourth position 9].
1*9*8*7 +9*1*8*7 +9*8*1*7 +9*8*7*1
4[1*9*8*7] answer

Arthur