Correct Answer - 5400
We have to select 4 professors for Roorkee and 6 professors for outside. Again, 2 professors prefer Roorkee and 3 outside, so we are left with 5 professors.
The number of ways in which two more professors for Roorkee can be selected is ` .^(5)C_(2)=10`.
And remaining 3 professors are left for outside. Now, 6 professors outside Roorkee can be allotted to 3 centres in `6!//(2!2!2!3!)xx3!` ways.
Now, 4 professors for 2 centers in Roorkee can be allotted in `4!//(2!3!3!)xx2!` ways. hence, the total number of ways is
`10xx(6!)/(2!2!2!3!)xx3!xx(4!)/(2!2!2!)xx2!=5400`