yes it will be 6
Given $2$ process, and each need $3$ resource and also given resource number $1,2,3$
Now, to get deadlock free execution of all $2$ process , we need minimum 2+2+1=5 resources
Say for process $1$ resource number $R_{11},R_{12},R_{13}$
and for process $2$ resource number $R_{21},R_{22},R_{23}$
So, number of ways possible
$R_{11},R_{12},......,R_{21},R_{22},R_{23}$
$R_{11},R_{12},R_{13},R_{21},R_{22},......$
$R_{11},......,R_{13},R_{21},R_{22},R_{23}$
$R_{11},R_{12},R_{13},R_{21},.......,R_{23}$
$.......,R_{12},R_{13},R_{21},R_{22},R_{23}$
$R_{11},R_{12},R_{13},.......,R_{22},R_{23}$
There 6 ways we can select 5 resource from total 6 resource