Question
How many strings of four decimal digits (Note there are 10 possible digits and a string can be of the form 0014 etc., i.e., can start with zeros.)
(a) have exactly three digits which are 9s?
(a) have exactly three digits which are 9s?
Answers
MathMate
Think of 3 9's to which we have to insert a fourth digit x(which is not a nine).
This can be in the four following ways.
X999 or 9X99 or 99X9 or 999X
In each case X can represent 9 possible digits including 0 but excluding 9.
So the number of strings is 4*9=36.
This can be in the four following ways.
X999 or 9X99 or 99X9 or 999X
In each case X can represent 9 possible digits including 0 but excluding 9.
So the number of strings is 4*9=36.