Question

By using the digits $1,2,3,4,5,6$ four digit numbers are formed. If a number is selected from them then the chance that the number reads alike from left to right and right to left is

• A. $\frac{1}{36}$
• B. $\frac{1}{6}$
• C. $\frac{1}{1296}$
• D. $\frac{1}{216}$

Answer 1

The correct option is A $\frac{1}{36}$

No. of ways of creating a $4$-digit palindrome = $6\times 6\times 1!=36$
(Since the last $2$ digits must match the first $2$ digits, the choice for the last $2$ digits are $1$ each)
Hence, probability = $\frac{36}{6\ast 6\ast 6\ast 6}=\frac{1}{36}$