Can you please explain this?
I understand that we divide the slots! to remove identical stuff but here how does it make sense?
This is the logic behind this step:
Say there are 4 boys: A, B, C, D
There are two ways of splitting them in two groups.
The two groups can be made in the following ways
1. AB and CD
2. AC and BD
3. AD and BC
The groups are not named/distinct. You have 4 boys in front of you and you split them in 2 groups and do not name the groups. There are 3 total ways of doing this.
On the other hand, I could put them in two distinct groups in the following ways
1. Group1: AB, Group2: CD
2. Group1: CD, Group2: AB (If you notice, this is the same as above, just that now AB is group 2)
3. Group1: AC, Group2: BD
4. Group1: BD, Group2: AC
5. Group1: AD, Group2: BC
6. Group1: BC, Group2: AD
Here I have to put them in two different groups, group 1 and group 2. AB and CD is not just one way of splitting them. AB could be assigned to group 1 or group 2 so there are 2 cases. In this case, every 'way' we get above will have two possibilities so total number of ways will be twice.
So there will be 6 total ways.
Here since the groups are not distinct but 8C2 * 6C2 * 4C2 * 2C2 makes them distinct (we say, select the FIRST group in 8C2 ways, SECOND group in 6C2 ways etc), we need to divide by 4!.
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