Find the number of ways this can be arranged in which no 2 women and no 2 men sit together given 4 men and 3 women are seated in a dinner table?
@Edit: They are seating in a row dinner table
I have applied 2 approaches in this question and found both approaches differ according to the Ans The Ans is 144
I want to ask why the second approach is wrong?
My 1st Approach:
When i do arrangement like this: first arrange all 3 women at alternate places i.e at 2 4 6 or 1,3,5.
Now the next 4 places ca be filled in 4! ways.
So,the required arrangement=4! .3!=144 Ans
When i do arrangement like this: first arrange all 4 men at alternate places i.e at 2 4 6 8 or 1 3 5 7.
Now,arrange the 3 Women can be placed at 5 places=5P3=60
The required arrangement=60 . 24=1440