In a)
In b) can the first digit be zero? Such as 06453.
If yes, then your answer is correct.
If not then it should
How many strings of five decimal digits
a. begin with an odd digit?
my answer)
b. do not contain the same digit twice?
my answer)
c. have exactly three digits that are 9s?
my answer)
that's 5.2=10 places for remaining 9 digits
and 9 choices for each place = 10x9 = 90, but,
can't it be like this....
exactly 3 same digits means ?
d. contain exactly three distinct digits?
my answer) 10.9.8.7.10
Hello, robocop_911!
Since it says "strings" rather than "five-digit numbers",
. . I assume they can begin with zero.
How many strings of five decimal digits
c. have exactly three digits that are 9's?
There are ways to place the 9's.
The other two places can be filled in ways.
My answer: .
This takes a bit more work . . .d. contain exactly three distinct digits?
The string is of the form: .
Form (1): .
There are choices for the three digits.
Then we decide which digit is the "triple": 3 choices.
And the five digits can be arranged in: . ways.
. . There are: . strings of the form
Form (2): .
There are choices for the three digits.
We we decide which two digits are the "pairs": 3 choices.
And the five digits can be arranged in: . ways.
. . There are: . strings of the form
Therefore, there are: . strings with exactly three distinct digits.