combination

peterand 8 of his friends are divided into 3 groups for preparing a Christmas party. 1 of them decorated a Christmas tree,4 of them prepare the Christmas dinner and the remaining 4 goto buy christmas presents.
if peter does not decorates the christmas tree and 2 particular friends must bein the same group, find the number of ways of forming the groups.


If Peter and the 2 particular friends are in the same group:
Out of the "dinner" and "presents" groups, Peter chooses 1group (2C1).
The 2 particular friends go to the same group (1C1).
Out of the rest 6 friends, choose 3 to form the "tree" group (6C3).
The rest 3 friends form the last group (3C3).

If Peter and the 2 particular friends are in the different groups:
Out of the "dinner" and "presents" groups, Peter choose 1group (2C1).
Out of the rest 6 friends, choose 2 to form a group with Peter (6C2).
Put of the rest 2 groups, the 2 particular friends choose a group (2C1)
Out of the rest 4 friends, choose 1 to form a group with the 2 particularfriends (4C1).
The rest 3 friends form the last group (3C3).

Total number of ways of grouping
= 2C1*1C1*6C3*3C3+ 2C1*6C2*2C1*4C1*3C3
= 2*1*20*1 + 2*15*2*4*1
= 40 + 240
= 280

The answer of my calculation is also 280.