Question

A palindrome is a number that reads the same left to right as it does from right to left, such as 131. How many 6-digits palindromes are there which are even?
a. 200
b. 400
c. 300
d. 500
e. None of these​

Answer 1

Answer:

(b) 400 is right answer

Step-by-step explanation:

I hope this is right!!!!

Answer 2

Step-by-step explanation:

All even numbers end with either of 0, 2, 4, 6 and 8. Now, a six digit even palindrome can’t end with 0 as the palindrome, as the ending digit is same as the starting digit and if the starting digit is 0 then it would be at best a 5 digit palindrome but not a six digit palindrome.

Thus, for a 6 digit even palindrome, the number has to start with 2 or 4 or 6 or 8 as it has to end with 2 or 4 or 6 or 8.

Thus, we have 4 possibilities for the 1st or the starting digit. we have 10 possibilities for the 2nd and 3rd digit respectively and then we just have the repeat of digits in reversed order and thus they can be chosen in only 1 way.

So, we have 4*10*10*1*1*1 = 400 different 6 digit even palindromes.