How many positive integers less than 1000 are there which contain at least one 4 or at least one 9 (or both)?
Obviously theres 100 in 400's and 900's but short of counting every other number whats the quickest way to work this out?
combinatorics
How many positive integers less than 1000 are there which contain at least one 4 or at least one 9 (or both)?
Obviously theres 100 in 400's and 900's but short of counting every other number whats the quickest way to work this out?
Best Answer
There are $8^3-1$ numbers that contain neither $4$ nor $9$. (The $-1$ is because $000$ doesn't count).
Subtract that from the total number of integers less than $1000$.
Of course, since $0$ doesn't have a $4$ or $9$ anyway, you could equally well ask about non-negative integers less than $1000$, in which case you'd just subtract $8^3$ from $10^3$, getting the same result.