Answer to Question #149677 in Discrete Mathematics for Elai

Question

A palindrome number is a number that is read similarly backwards. How
many possible 5-digit palindromic numbers are there?
A. 608
B. 648
C. 688
D. 728

Answer 1

$\text{let }x_1,x_2,x_3,x_4,x_5 \text { digit palindrome }$,

$x_1=x_2,x_2=x_4,x_3 =x_3\, \text{equality defined when reading palindrome in reverse}$

$\text {that is, the palindrome is uniquely determined by the choice of numbers }x_1,x_2,x_3$ ;

$x_1 \text{ can be selected from 9 digits,}$

$\text{0 is excluded because the palindrome is five digits}$ ,

$x_2,x_3 \text{ can be selected from 10 digits}$ ,

$\text{the number of combinations will be }9*10*10=900$ ,

$\text{the number of 5 digit palindromes are }\,900$ ,

$\text {all the suggested answer options are not correct.}$

Answer: 900 the number of 5 digit palindromes, all the suggested answer options are not correct