anud33p wrote:
Could you please help me find the glitch in my approach.
I understand the logic mentioned above but I would like to know what is wrong with:
1. First placing three Gnomes: G G G
2. Now, there are four places to fit in three Elves. Number of ways to select three out of four places = 4C3
3. Permute the three genomes and three elves = 4C3 * 3! * 3!
By this approach, the answer I get is 144. What is wrong? o. O
Thank you!
Hi,
I hope it is not too late.
The error in this is approach is that by performing 4C3 you are selecting any 3 spaces out of 4 which is not be the desired requirement.
Let's say that we have already arranged the Gnomes.
_G_G_G_
1 2 3 4
Now we have 4 places where the elves can sit. By performing 4C3 we are selecting any 3 spaces.
But what if we select 1st,3rd and 4th number spaces for the Elves to sit?
That is :
E G G E G E
1 3 4
This is wrong as the question requires the Gnomes not to sit along each other.
Hence the best approach for this question would be :
1. EGEGEG: 3!x 3! =36
2. GEGEGE: 3!x 3! =36
total ways=36+36=72
Hope that helps.