Explanation:
A Given,
Sum of the given digit is
\(=0+1+2+5+7+9=24\)
Now, 6 digit number ( \(\mathrm{b} \mathrm{c} d\) e f) are divisible by 11 . \(|(a+c+e)-(b+d+f)|\) is a multiple of 11
Therefore,
\(\mathrm{a}+\mathrm{c}+\mathrm{e}=\mathrm{b}+\mathrm{d}+\mathrm{f}=12\)
\(\text { Case }(\mathrm{I})(\mathrm{a}, \mathrm{c}, \mathrm{e})=(7,5,0)\)
\(\quad(\mathrm{d}, \mathrm{d}, \mathrm{f})=(9,2,1)\)
\(\quad 2 \times 2 \times 1 \times 3 \times 2 \times 1=24\)
Case (II)
\((\mathrm{a}, \mathrm{c}, \mathrm{e})=(9,2,1)\)
\((\mathrm{b}, \mathrm{d}, \mathrm{f})=(7,5,0)\)
\(3 \times 2 \times 1 \times 3 \times 2 \times 1=36\)Total numbers \(=24+36=60\)