hi guys,
after some tough hours with combinatorics and counting I am proud to finally state that i got to understand these topics a little better. Thus, the difference between permutations and combinations, as well as their respective use, are pretty much clearer to me.
However, I have one more questions:
when do we use only 7! or rather N! ?
It is clear to me that when you are counting the possible number of ways 6 people can sit next to each other you should calculate 6!. Or the examples wth the menus in a restaurant. But is there a general rule or a hint when to use only the N! ?
The way I understand it is:
you should proceed only with N! (namely, w/o dividing it by other factoriels) when you care for only 1 item of a set. one meal, one person etc. Thus, if you want to take 1 person from a group of ten, it is basically = 10! / ( 9! * 1! ), or simply 10. If you'd like to take the possible scenaris of getting 2 people out of a group, though, (w/o accounting for a particular order) the expression from above becomes: 10! / ( 8! * 2!), which is dfferent from 10 and that is why we write down the factoriels in the denominator.
It will be very helpful if someone could only tell me if i ve gotten this he right way, it is rather different.
thank you in advance and... off to probabilties.
)
after some tough hours with combinatorics and counting I am proud to finally state that i got to understand these topics a little better. Thus, the difference between permutations and combinations, as well as their respective use, are pretty much clearer to me.
However, I have one more questions:
when do we use only 7! or rather N! ?
It is clear to me that when you are counting the possible number of ways 6 people can sit next to each other you should calculate 6!. Or the examples wth the menus in a restaurant. But is there a general rule or a hint when to use only the N! ?
The way I understand it is:
you should proceed only with N! (namely, w/o dividing it by other factoriels) when you care for only 1 item of a set. one meal, one person etc. Thus, if you want to take 1 person from a group of ten, it is basically = 10! / ( 9! * 1! ), or simply 10. If you'd like to take the possible scenaris of getting 2 people out of a group, though, (w/o accounting for a particular order) the expression from above becomes: 10! / ( 8! * 2!), which is dfferent from 10 and that is why we write down the factoriels in the denominator.
It will be very helpful if someone could only tell me if i ve gotten this he right way, it is rather different.
thank you in advance and... off to probabilties.
)
