shankar245 wrote:
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.
Method I
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.
Method II
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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Karishma
Veritas Prep GMAT Instructor
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