How many three-digit positive integers have at least one prime digit?

So I thought it would be easier to start counting the numbers that do not have any prime digits.

Jasonkiln Aug 2, 2022

#1**+2 **

Here's my best attempt (I'm not great at these counting problems !!! )

Non-prime digits = (0, 1, 4, 6, 8, 9 )

Number of three digit numbers not having any prime digits

Hundreds place = (Choose any one of the digits 1,4,6,8,9) = C(5,1) = 5

Tens place = ( Choose any one of the digits 0,1,4,6,8,9) = C(6,1) = 6

Ones place = (Choose any one of the digits 0,1,4,6,8,9) = C(6,1) = 6

So 5 * 6 * 6 = 180 have no prime digits

So

900 three digit numbers - 180 with no prime digits =

720 have at least one prime digit

CPhill Aug 2, 2022

#2**+1 **

There are \(900 - 5 \times 6 \times 6 = \color{brown}\boxed{720}\) numbers with at least 1 prime digit.

BuilderBoi Aug 2, 2022