# probability rules

#### prsndwg

7+ Year Member
Can somebody help me understand what the difference b/w premutation rule and combination rule please?

I am tired of guessing which one to use without knowing the exact usage of them..

nPr= N!/(N!-R!) and also nCr=N!/(N-R)! (R!)

If there is anyother ones with "!" please let me know about them..

#### navneetdh

Can somebody help me understand what the difference b/w premutation rule and combination rule please?

I am tired of guessing which one to use without knowing the exact usage of them..

nPr= N!/(N!-R!) and also nCr=N!/(N-R)! (R!)

If there is anyother ones with "!" please let me know about them..

Ok i use the following:

Permutation counts the number of ways n objects can be placed in k spots in order. Like how many 4 letter long words can you make from the first 10 letters of the alphabet.
Note that here order does matter. If you choose the letters BAG vs GAB. They are 2 different words.

Vs. In combinations order will not matter. COmbinations is looked at more like a group. Like you have a group of 3 letters. so G,A,B or B,A,G or A,G,B or B,G,A are all 3 letters but in permuations each of these will count seperately. But in combinations they count only once because they are a group of the same 3 letters.

So in combinations you count the number of groups of k objects you can make form a total of n objects.
Ex: how many teams of how many teams of 5 players will you make from a group of 11 players.

so think if i have players jack, jim jill jake joe in a team, will it be same as having joe jake jill jim and jack? yes. it will be the same team. SO it doesnt matter how I order them in the team, it is still the same team. So it will be combinations

Also another thing i try to think is that, when order matters that is when tab is diff from bat is diff from abt then i can have more number of things from the same 3 letters or objects. This is permutation

In combination order doesnt matter so everything with same objects counts as one. So I have lesser. So in combination formula you see another term in the denominator. SO you denominator is bigger and this will make your whole fraction smaller. SO lesser groups. Thus combinations.

I hope that helps

combination

10+ Year Member

OP

#### prsndwg

7+ Year Member
Thanks for clarifying it

Ok i use the following:

Permutation counts the number of ways n objects can be placed in k spots in order. Like how many 4 letter long words can you make from the first 10 letters of the alphabet.
Note that here order does matter. If you choose the letters BAG vs GAB. They are 2 different words.

Vs. In combinations order will not matter. COmbinations is looked at more like a group. Like you have a group of 3 letters. so G,A,B or B,A,G or A,G,B or B,G,A are all 3 letters but in permuations each of these will count seperately. But in combinations they count only once because they are a group of the same 3 letters.

So in combinations you count the number of groups of k objects you can make form a total of n objects.
Ex: how many teams of how many teams of 5 players will you make from a group of 11 players.

so think if i have players jack, jim jill jake joe in a team, will it be same as having joe jake jill jim and jack? yes. it will be the same team. SO it doesnt matter how I order them in the team, it is still the same team. So it will be combinations

Also another thing i try to think is that, when order matters that is when tab is diff from bat is diff from abt then i can have more number of things from the same 3 letters or objects. This is permutation

In combination order doesnt matter so everything with same objects counts as one. So I have lesser. So in combination formula you see another term in the denominator. SO you denominator is bigger and this will make your whole fraction smaller. SO lesser groups. Thus combinations.

I hope that helps

combination

OP

#### prsndwg

7+ Year Member
Can you please solve this using these formulas?

If 4 ppl are arranged at random in a line, what is the probabilty of 2 particular being next to eachother??