Alphabet palindrome * no. not a palindrome + Alphabet not a palindrome * no. a palindrome.

For alphabet to be a Palindrome, lets take one alphabet for ex: A,any of the 26 letters,A. For 26 alphabets it should be 26(1*26*1) = 26^2

For alphabet not to be a palindrome, lets take one alphabet for ex: A, any of the 26 letters, any of the 25 letters except A.
For 26 Alphabets it should be 26(1*26*25)

For number to be a palindrome, same type of calculation will result in: 10(1*10*1)
For number to be not a palindrome: 10(1*10*9)

total = 26(1*26*1)*10(1*10*9) + 26(1*26*25)*10(1*10*1) = 26^2 * 10^2*9 + 26^2 * 25 * 10^2

Total possible combinations = 26^3 * 10^3

Probability = Total / Total possible combinations

= (26^2 * 10^2*9 + 26^2 * 25 * 10^2)/26^3 * 10^3

= 17/130

OA - C

a quick answer..
Since the palindromes are only 3 letters or digits, the probability would depend on the third digit/letter

so

1) \(L_1-L_2-L_3-D_1-D_2-D_3\)---------- 26-26-1-10-10-9
when palindrome is with letters, the 3-digit number can have any of remaining 9 digits in units digit, as it has to be different from the first digit \(D_1\)
2) \(L_1-L_2-L_3-D_1-D_2-D_3\)---------- 26-26-25-10-10-1
when palindrome is with digits, the 3-letter formed can have 25 ways in third place, \(L_3\), different from the first digit \(L_1\)
so total ways 9+25=34

while in total ways these number will be 26*10=260

P = \(\frac{34}{260}=\frac{17}{130}\)

C
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