easy way to remember which formula to use among: aCn, aPn, and n!

Question

I have gone through the GMAT club Math book, and I know it states that we need to first figure out what the questions asks rather than ponder on which formula to use, but I still get confused about which formula to use, esp for the 'selecting a committee' / 'selecting x from y' etc.

I also get confused scenarios where to use the aCn formula and the (I don't know what it is called) n x (n-1) x (n-2) x (n-3) formula

example: 
Q. From a group of 8 members, 4 are to be selected to form a committee.
- My thought process:
I get confused whether to use 8C4 or do 8x7x6x5

Is there an easy method to identify when to use each of these formulas:

nCa
nPa
n!
n x (n-1) x (n-2)...

chetan2u · Answer

Hi...

1) when you are selecting say 3 things out of n things, it is nC3. Here a,b,c is same as b, c,a..
2) when you are arranging say 3 things out of n things, it is nP3. Here a, b, c is different from b, a, c..
It is also same as n*(n-1)*(n-2)....
3) n! Is when you are arranging all n of n things... Same as n*(n-1)*(n-2)*.....3*2*1

ameyaprabhu · Answer

Hi  chetan2u ,

I am still a little confused here.

You have mentioned we need to use nPa for arrangements, but the GMAT club Math book says we need to use this formula for "choosing", albeit for an ordered collection.

How do we differentiate between ordered and unordered?

chetan2u · Answer

Hi..
Arrangements too mean that the order the items are placed is important..
It is same as choosing but with order important.

Now difference in ordered and unordered.
Unordered..
1) choose a team of 11 from 16.
2) way to eat 5 different sweets out of 7 that are available.
Here who you choose first or what you eat first does NOT matter.

Ordered...
1) ways to seat 11 person out of 16.
2) ways to place 5 sweets in 5 different shaped boxes.
Here who sits on which chair is important.

ameyaprabhu · Answer

Hi  chetan2u ,

I think that solves my query, thank you so much.

So do you think this is the right thought flow to identify which formula to use (sorry if I am bothering with too many questions, but my exam is 11 days away, and so far P&C is my biggest weakness :!: )

1. identify whether it is an 'arrangement' question or 'select question'

2. if it is an 'arrangement' question, we have to use the Permutation formula, or the n! formula (divide by a! where a=similar elements)

3. if it is a 'choose' / 'select' question then first identify whether it matters how we choose. If order matters, i.e. abc is not the same as cab then select use combination formula. If order doesn't matter then use the permutation formula

Is there anything I am missing?

easy way to remember which formula to use among: aCn, aPn, and n!

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