Question

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

Answer 1

The number should be of the form $ABCDCBA$

Number of ways of selecting $A$ are $4$ as the possible digits are $1,2,3,4$.

Number of ways of selecting $B$ are $5$ as $0$ is also a possibility.

Similarly

Number of ways of selecting $C$ is $5$

Number of ways of selecting $D$ is $5$

Hence the number of ways $=4\times 5\times 5\times 5=500$