- #1

cragar

- 2,552

- 3

## Homework Statement

social security number is a 9 digit number.

the first digit may be 0

a. How many numbers are available

b. How many are even

c. How many have all of their digits even

d. How many read the same forward and backward

e. How many have none of their digits equal to 8

f. How many have at least one digit equal to 8

g. How many have exactly one 8.

## The Attempt at a Solution

a. assuming we can have a number with all zero's i would say

[itex] 10^9 [/itex] because we have 10 possible choices for each of the 9 slots

b. I would assume half of part a

c. I would assume half unless there is some kind of fence post error.

d. I think it is 10*10*10*10*10*1*1*1*1

The middle number can be what-ever since its in the middle

so i have 10 choices for that. And the four numbers to the left of the middle can be anything so i have 10 choices for those but this restricts the numbers on the right so I have only 1 choice or those.

e. Since i have removed a possible choice I only have 9 choice for my 9 slots so it should be [itex] 9^9 [/itex]

f. this should be [itex] 10^8 [/itex] because on one of them I only have one choice but the rest I have 10 choices.

g. On one of the slots I have one choice because it hast to be an 8 , but the rest can't have an 8 in them therefore I have 9 choices on the remaining 8 digits so the answer should be [itex] 9^8 [/itex]