Question

The number of $6$ digit numbers that can be formed using the digits $0,1,2,5,7$ and $9$ which are divisible by $11$ and no digit is repeated, is:

• A. $36$
• B. $60$
• C. $48$
• D. $72$

Answer 1

Answer: (B)

$60$

Sum of given digits $0,1,2,5,7,9$ is $24$.
Let the six digit number be abcdef and to be divisible by $11$.
So $|(s+c+e)-(b+d+f)|$ is multiple of $11$.
Hence only possibility is $a+c+e=12=b+d+f$
Case - I $\{a,c,e\}=\{9,2,1\}\&\{b,d,f\}=\{7,5,0\}$
So, Number of numbers $=3!\times 3!=36$
Case - II $\{a,c,e\}=\{7,5,0\}$ and $\{b,d,f\}=\{9,2,1\}$
So, Number of numbers $2\times 2!\times 3!=24$
Total $=60$