Consider the following question:
A committee of $4$ is to be chosen from $7$ people. $2$ of the $7$ people cannot work together. How many committees are possible if the two do not work together.
Here is how I am solving it
Total No. of possibilities = With Enemies + Without Enemies
Total No. of possibilities = $\tbinom{7}{4} = 35$
With Enemies (I considered the workers who are enemies as a single unit) = $\tbinom{6}{4} = 15$
Now I am getting $35-15 = 20$ which is wrong, I was suppose to get $25$. Could anyone tell me where I am going wrong ?