saiesta wrote:
mau5 wrote:
arakban99 wrote:
A palindrome is a number which reads the same when read forward as it it does when read backward. So, how many 5 digit palindromes are there?
(A)720
(B)800
(C)890
(D)900
(E)950
A 5 digit palindrome would look like this : \(abcba.\)
Thus, the first digit can be filled in 9 ways(1-9), the second digit can be filled in 10 ways (0-9) and the 3rd digit can again be filled in 10 ways. The last 2 digits would just mirror the already selected digit. Thus, the no of ways : 9*10*10*1*1 = 900.
D.
I understand that a 5 digit palindrome would look like \(abcba\). However, a 5 digit palindrome could also look like \(aaaaa\) or \(ababa\). Why are we not adding the combinations of these two palindromes to our answer?
The cases you are mentioning are already covered in the solution above. Lets say you have the form of abcba, then for the first digit you have 9 ways, for second digit ('b') you have 10 digits and finally for c again, you will have 10 ways giving you a total of 9*10*10*1*1 = 900 ways.
aaaaa and ababa are already covered in the above scenarios for example lets say, a = 5, then for b we can again have 5 as we have all 10 digits allowed. Repeat the same for 'c' and you will get your aaaaa combination. Same logic applies to ababa as well.
Hope this helps.