SOLUTION: Can someone help me please?? Thank You!! 20) H ow many different sequences of 4 digits are possible if the first digit must be 3, 4, or 5 and if the sequence may not end in 000?

Question 418849: Can someone help me please?? Thank You!!
20) H ow many different sequences of 4 digits are possible if the first digit
must be 3, 4, or 5 and if the sequence may not end in 000? Repetition of
digits is allowed.
A) 2 ,997
B) 2 ,999
C) 2 ,000
D) 1 ,512
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
I would compute all the possibilities as if there
were no restrictions. Then I would subtract the
choices that are not allowed
-----------------
With no restrictions:

---------
0,1,2,6,7,8, and 9 are not allowed
for the 1st digit. That is
not allowed
---------
With the last 3 digits 0,
not allowed

------------------
Now the tricky part: When I tested for sequences not allowed
did I count some things twice ? If I did, I have to add those back in.
The not allowed includes
0000, 1000, 2000, 6000, 7000, 8000, and 9000
so, I must add these back in
answer

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