How many 5-digit numbers have at least one 2 or one 3 or one 4 among their digits?

Guest Jan 7, 2021

#1**0 **

There are 10 different number 0-9. There are three digits and you want at least one to appear. That means the odds are 3/10.

Guest Jan 7, 2021

#3**0 **

the question didn't ask for the odds, it asked for the number of 5 digit numbers satisfying the statement.

Instead of counting the number of 5 digit numbers satisfying the statement, count the ones that *don't *satisfy the statement and subtract from the total number of possibilities.

For the first digit, there are 9-3=6 possibilities, and for the rest of the digits, there are 10-3=7 possibilities. Therefore the total of numbers that don't satisfy the statement is equal to 6*7*7*7*7 = 14406.

The total number of possibilities is just 9*10*10*10*10=90000.

Subtracting, we get the answer:

**75594 **5-digit numbers.

Guest Jan 7, 2021