Ex 2.21 grading questions

There are ten teaching assistants available for grading papers in a calculus course at a large university.
The first exam consists of four questions in increasing order of difficulty,
the professor wishes to select a different assistant to grade each question
- (only one assistant per question).
In how many ways can the assistants be chosen for grading?
Here
- $n =$ group size $= 10$ and
- $k =$ subset size $= 4$ .
The number of permutations is $$ {P}_{4,{10}} = \frac{{10}!}{\left( {{10} - 4}\right) !} = \frac{{10}!}{6!} = {10}\left( 9\right) \left( 8\right) \left( 7\right) = {5040}

- T ha t i s, t h e p ro f essorco u l d g i v e 5040 d i ff ere n t f o u r - q u es t i o n e x am s w i t h o u t u s in g t h es am e a ss i g nm e n t o f g r a d ers t o q u es t i o n s, - b y w hi c h t im e a llt h e t e a c hin g a ss i s t an t s w o u l d h o p e f u ll y ha v e f ini s h e d t h e i r d e g ree p ro g r am s!

Youliang Zhong