[crazy problem] probablity zip code?

Question

A Newspaper resporter described the old rules for the telephone area codes by writing

"possible area codes with 1 or 0 in the second digit (Excluded: codes ending in 00 or 11, for toll-free calls, emergency services, and other special uses.)"
Codes beginning with 0 or 1 should also be excluded.

How many different area codes were possible under these old rules?

Answer 1

The area codes are three digit numbers

First number - excludes 0 or 1
Second number - must be 0 or 1
Third number - anything except matching the second number

Number of possible area codes

If second number is 0
8*1*9

If second number is 1
8*1*9

Total = 2*8*1*9 = 144

There were 144 possible area codes under the old rules.

Answer 2

Hi,

If you could use any of the 10 digits from 0 - 9 in all 5 spots, there would be 10 * 10 * 10 * 10 * 10 = 100,000 of them. But, because there are restrictions, this number decreases.

Since codes beginning with 0 or 1 should be excluded, the first spot doesn't have 10 choices - it only has 8. So the total number of area codes would be down to 8 * 10 * 10 * 10 * 10 = 80,000.

Then if the second position must be either a 0 or a 1, there are only 2 choices there, giving 8 * 2 * 10 * 10 * 10 = 16,000.

The last 2 positions right now could have 10 * 10 or 100 variations, but of those 100, two must be excluded - those ending in 00 or in 11, meaning there are only 98 choices for the combined spot for what was the last 2 columns. This gives
8 * 2 * 10 * 98 = 15,680

So, altogether there are 15,680 telephone area codes that are possible.

I hope that helps!! :-)

Answer 3

Telephone area codes have three digits. The first digit is simply restricted to being from 2-9 (eight choices).

The second digit is either 0 or 1 (two choices).

The last digit can be any digit (ten choices).

So, before excluding 00 and 11 endings, we have 8 * 2 * 10 or 160 choices.

Each first digit has two special endings that must be excluded (00 and 11). There are eight first digits. So, we must exclude 8 * 2 or 16 special codes.

160 - 16 = 144 area codes by these rules.