The number of distinct ways she can do this is:
6635520 ways
If we have to chose r items out of a total of n items then the number of ways of doing so is given by:
[tex]n_C_r=\dfrac{n!}{r!\times (n-r)!}[/tex]
There are 24 students in Mrs. Noether's third grade class.
Now, Mrs. Noether wants to assign 8 students to Book A.
This means that the number of ways of doing so is:
[tex]{24}_C_{8}[/tex]
10 students are to be assigned to Book B.
The number of ways of doing so is:
[tex]{24}_C_{10}[/tex]
and 6 students to Book C.
The number of ways of doing so is:
[tex]{24}_C_{6}[/tex]
Hence, the total number of distinct ways of doing so is:
[tex]{24}_C_{8}\times {24}_C_{10}\times {24}_C_{6}[/tex]
which on solving gives:
6635520 ways
