Question

Find the total number of ways in which a 3- digit number xyz can be formed from the digits $1,4,5,6,7,8and9$ such x,y,z that are in A.P and $x\ne y\ne z.$

Answer 1

$x,y,z$ are in $A.P$

$x+z=2y$

Possible arrangements are

$147,741,159,951,678,876,456,654468,864,567,765,579,975$

Total $=14$ ways