Question

Find the number of seven digit palindromes that can be formed using 0, 1,2,3,4.

Answer 1

Hint: Palindrome numbers are the number which when read from forward or the backward are the same.
In this question we are given the 5 digits using which we have to form a 7 digit number which should be in palindrome and as in forward and reverse number are the same so we will find the ways of forming each digit of the palindrome number.

Complete step-by-step answer:
Let the seven digit number formed by using 0, 1, 2, 3, 4 be ABCDCBA
We can see ABCDCBA is a palindrome, since when it is read from forward and backward are the same as ABCDCBA and ABCDCBA
Now we will form the number using the digits 0, 1,2,3,4
Now since we know a valid number cannot start with 0, we can say the first digit A will be selected from 1,2,3,4 so the number of ways of selecting A is \[ = 4\]
Now for the second digit, selecting 0 is valid so the number of ways of selecting B from 0, 1,2,3,4 will be \[ = 5\]
Now for the third digit, the number of ways of selecting C from 0, 1,2,3,4 will be \[ = 5\]
Now for the fourth digit, the number of ways of selecting D from 0, 1,2,3,4 will be \[ = 5\]
Hence the number of ways selecting the number will be
 \[ = 4 \times 5 \times 5 \times 5 = 500\;ways\]
Therefore, the number of seven digit palindromes that can be formed using 0, 1,2,3,4
\[ = 500\;ways\]
So, the correct answer is “500 ways”.

Note: Finding the numbers of ways to form a number in palindrome is same from forward and the backward so we can say \[500ways\] will be same if we even find the number of seven digit palindromes that can be formed using 0, 1,2,3,4.