(12 x 11 x 10 x 9)/(4 x 3 x 2 x 1) = 11,880/24 = 495 different groups.
Three groups every time.
495/3 = 165 ways for the different groups to stand.
There are 5040 ways.
3 students can be chosen from a class of 30 in (30 x 29 x 28) = 24,360 ways.But each group of the same 3 students will be chosen in six different ways.The number of different groups of 3 is 24,360/6 = 4,060 .
7
20*19*18*17*16 = 1860480 ways.
I Dont Know [210]
they can be 2 groups of 16, 4 groups of 8, 8 groups of 4, or 16 groups of 2
There are five ways to do this, if you include 32 'groups' with one member each.The others are 2 groups of 16, 4 groups of 8, 8 groups of 4 and 16 groups of 2.
2 groups of 16, 4 groups of 8, 8 groups of 4, 16 groups of 2. Not really divided or in groups, but there could be 1 group of 32 or everyone by themselves.
150
The formula would be: (40!/36!)/4! This gives 2193360/24, or 91,390 unique groups.
6.4
There are only two possibilities... 10 groups of 2 or 5 groups of 4. Unless - you can have varying sized groups - which you didn't specify.
7
One side is labled North, and the other side is labled South
There are 19 ways to do this.
There are 5040 ways.
3 students can be chosen from a class of 30 in (30 x 29 x 28) = 24,360 ways.But each group of the same 3 students will be chosen in six different ways.The number of different groups of 3 is 24,360/6 = 4,060 .