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

Question

3 years ago

13

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?

Mathematics

1 answer:

denis-greek [22] · Answer 1 · 2022-08-22T00:30:15+03:00

Answer:

<em>19800 seconds, or 330 minutes, or 5 hours + 30 minutes</em>

Step-by-step explanation:

<u>Number Permutations</u>

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