Mark can remember only the first 4 digits of his friend's phone number. He also knows that the number has 7 digits and that the last digit is not a 0. If Mark were to dial all of the possible numbers and if it takes him 22 seconds to try each one, how long would it take to try every possibility?

19800 seconds, or 330 minutes, or 5 hours + 30 minutes

Step-by-step explanation:

Number Permutations

We know the phone number has 7 digits, 4 of which are known by Mark. This leaves him 3 digits to guess with. We also know the last one is not zero. The number can be represented as

XXY

Where X can be any digit from 0 to 9 and Y can be any digit from 1 to 9. The first two can be combined in 10x10 ways, and the last one can be of 9 ways, this gives us 10x10x9 = 900 possible permutations.

If each possible number takes him 22 seconds, every possibility will need

22x900=19800 seconds, or 330 minutes, or 5 hours + 30 minutes