Question

How many 9 digit palindromes are there with all the digits being even and each digit appearing no more than once

Answer 1

96

Explanation:

We have to find number of 9 digit palindromes when all digits are even and each digit appearing not more than twice.

Digits used here

0,1,2,3,4,5,6,7,8,9

Total number of even digits=0,2,4,6,8=5

Now,

0 cannot be used for first place if number is 9-digit number.

Firs place can be filled by number of ways=4

Second place can be filled by number of ways=4

Third place can be filled by number of ways=3

Fourth place can be filled by number of ways=2

Fifth place can be filled by number of ways=1

Total number of ways=
`4* 4* 3* 2* 1`

Total number of ways=96

Hence, total number of 9-digits palindromes when all digits are even and appearing not more than twice=96