00:01
In this question, we're given that there are 12 workers in an office with hugo and viviana among this 12.
00:08
And a group of five is to be chosen from these 12 workers.
00:13
Now, hugo and viviana refuse to work together.
00:17
So under this restriction, what is the number of different working groups of five that can be formed? before we answer this question, we have to decide whether it's a permutation or combination question.
00:28
Now take note that in the context of this question, the five chosen are without replacement.
00:42
And that always ask yourself, after we have chosen this five, do we need to arrange them in some order? is there a position we need to slot any one of them in? now in this question, there isn't.
00:55
So the order is not important.
01:01
So without replacement and order not important, we will be using combination, which is the c.
01:08
Now, if order is important, we have to use permutation, but in this case, it's combination, since the five of them is just chosen like that, doesn't need to be slaughtered in any arrangements.
01:22
So now, hugo and viviana refuse to work with each other, so it's really easier to do it a complementary way, that is to take the total number of possible working groups of five without any restriction, and we minus off the number of groups that can be formed if hugo and vivian are in it together.
01:45
So it would be equals to this.
01:58
So we have total number of groups of five that can be formed with no restriction, minus of the number of groups of five that can be formed with hugo and viviana in the group...