help me in maths...:)

All possible committees without any restriction are    8C3   x  7C4   =   1960

Committees when Mrs. X & Mr. Y are together are      7C2   x   6C3   =     420

So, committees when they are never together are  1960  -  420  =  1540

Majority decision against the lower court is possible in the following cases :

5 judges against the decision & 4 in favour   =   9C5   x   4C4   =   126

6 judges against the decision & 3 in favour   =   9C6   x   3C3   =     84

7 judges against the decision & 2 in favour   =   9C7   x   2C2   =     36

8 judges against the decision & 1 in favour   =   9C8   x   1C1   =       9

9 judges against the decision & 0 in favour   =   9C9   x   0C0   =       1

Total ways possible is the sum of all these                                       256

Let us place the 6 t's first. Since all the t's are identical there is no question of arranging them. Since no two '-' signs must be together there are 7 places to be selected to place the 4 t ' - ' signs. Since all the ' - ' signs are identical there is no question of arranging them.

Hence we need to select 4 out of 7 places. This can be done in 7C4 ways  =  35 ways

12 students are to be divided into 3 equal groups of 4 each.

This can be done in     12!  /  (3!  x  4!  x  4!  x  4!)      ways