I forget the exact expression of the questions. But the related details are exhaustive here.
it's about permutation and combination. By the way, I am not student, i am looking for explanation and understanding, not answers..
1. There are 6 people, namely A, B, C, D, E, F in a row, how many ways of arrangement are there such that person A,B,C must be separated
No equation given
The Attempt at a Solution
I especially paid attention to the word "must be separate", then I first count the number of ways that A,B and C "must be grouped" together. which result in 3! (arrangement within A,B,C) and then multiply 4! (taken ABC as one object).
Then for 6 people randomly arranged in order there are 6!. It's easy.
so the solution i think should be 6! - 3! x 4!
however, that was wrong. the solution is 3! x 4!
I feel so hard understanding why.
I don't know what they mean by "must be separate" here, how about, for example, A E F B C D? when B and C are combined while A is separate from them. Did I forgot to minus this possibility?
The answer is actually 144 but I get no idea about it.
I am not really clever, please explain in a simple way. Thanks people. Thanks people