How many five digit palindromes are there where the digit “1” appears at least once?

A 5 digit palindrome number must be written as

where are digits. We want "1" to appear at least once, which leads to the following cases:

Only one of the variable is equal to 1 (the other two are not)

In this case, the possible patterns of the numbers are . We have 9 choices for each of the non-one digits (all the reamaining digits). So, the count of these kind of number is

Two variables are equal to 1 (the third is not)

In this case, the possible patterns of the numbers are . We have 9 choices for the non-one digit (all the reamaining digits). So, the count of these kind of number is

All variables are equal to 1

In this trivial case we only have one number,

Total:

the answer is 18 units because there are 18 small cubes inside the rectangle

hope this and p.s i am also in k12

step-by-step explanation: