What does nCr stand for?

_nC_r calculates the number of combinations of sub-groups of size 'r' taken from an initial group of size 'n'.

For instance, if there is a group of 20 persons and 4 are chosen to represent that group, there will be ₂₀C₄ possible groups. 

When using combinations, order is not important -- there will be a group of 4 persons but the group of {Tom, Betty, Mary, Carl} is the same group as {Betty, Carl, Mary, Tom}.

It is calculated with this formula:  n! / ( r! · (n - r)! ).

Thanks Geno,

I'm just giving another example.

Say you have 5 b***s that are lettered as A,B,C, D and E

how many ways can you choose 3 or them

Let me see

ABC    ABD    ABE    ACD    ACE    ADE

BCD    BCE    BDE

CDE

that is 10 ways.  (assuming that I didn't double up or miss any)

5C3 is just this.   It is how many ways you can select 3 things out of 5 things so it must equal 10

check  

I'll enter    nCr(5,2)    into the web 2 calc.  :)

$${\left({\frac{{\mathtt{5}}{!}}{{\mathtt{3}}{!}{\mathtt{\,\times\,}}({\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{3}}){!}}}\right)} = {\mathtt{10}}$$

Oh and if you are doing it ny hand the calc just showed  you the formula :)