#1**+10 **

_{n}C_{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 _{20}C_{4} 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)! ).

geno3141
Mar 30, 2015

#1**+10 **

Best Answer

_{n}C_{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 _{20}C_{4} 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)! ).

geno3141
Mar 30, 2015

#2**+5 **

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 :)

Melody
Mar 31, 2015