1. Counting problems

Q How many strings of four decimal digits

a) do not contain the same digit twice
my ans: 4 x 9^2
b) end with an even digit
my ans: 5 x 10^3
c) have exactly three digits that are 9s

my ans: 4 x 9

Thanks for the help!

2. Originally Posted by robocop_911

Q How many strings of four decimal digits

a) do not contain the same digit twice
my ans: 4 x 9^2
b) end with an even digit
my ans: 5 x 10^3
c) have exactly three digits that are 9s

my ans: 4 x 9

Thanks for the help!
a) do not contain the same digit twice:
$10 \cdot 9 \cdot 8 \cdot 7 = 5040$

c) have exactly three digits that are 9's: Your answer is correct.

3. [QUOTE=robocop_911;151794]Q How many strings of four decimal digits
a) do not contain the same digit twice
my ans: 4 x 9^2 NO
b) end with an even digit
my ans: 5 x 10^3 YES
c) have exactly three digits that are 9s
my ans: 4 x 9 YES
Part (a) is a simple permutation: (10)(9)(8)(7). No repeated digits.

4. [quote=Plato;151796]
Originally Posted by robocop_911
Q How many strings of four decimal digits
a) do not contain the same digit twice
my ans: 4 x 9^2 NO
b) end with an even digit
my ans: 5 x 10^3 YES
c) have exactly three digits that are 9s
my ans: 4 x 9 YES
Part (a) is a simple permutation: (10)(9)(8)(7). No repeated digits.
Can you please explain why it won't be 4 x 9^2?
From what I think, there are 4 places for the same digit to occur twice in a 4 decimal digit and the remaining 2 places can contain any remaining 9 digits!

5. how did the answer come?

Can anyone "check" my following question answer...
Q How many strings of four decimal digits

a) have exactly three digits that are 9s
my ans: 4 x 9
How come is it 4x9 can anyone explain me that?

Thanks for the help!

6. There are 4 places to put the 'other' digit and 9 possible choices for that digit.

7. Originally Posted by Plato
There are 4 places to put the 'other' digit and 9 possible choices for that digit.
How come there are 4 places to put "other digits". We need to have "exactly" three 9s in the number!

Are you taking complement of the sentence or something?

8. X999
9X99
99X9
999X
Four places.