How many possible combinations for first ten finishers in a 24 man race

24C10      This is where order does not count    (combinations)

$${\left({\frac{{\mathtt{24}}{!}}{{\mathtt{10}}{!}{\mathtt{\,\times\,}}({\mathtt{24}}{\mathtt{\,-\,}}{\mathtt{10}}){!}}}\right)} = {\mathtt{1\,961\,256}}$$

 

24P10      This is where order does count     (permutations)

$${\left({\frac{{\mathtt{24}}{!}}{({\mathtt{24}}{\mathtt{\,-\,}}{\mathtt{10}}){!}}}\right)} = {\mathtt{7\,117\,005\,772\,800}}$$