I am having trouble solving this problem from my GRE practice set:
A reading list for a humanities course consists of 10 books, of which 4 are biographies and the rest are novels. Each student is required to read a selection of 4 books from the list, including 2 or more biographies. How many selections of 4 books satisfy the requirements?
I tried solving with (4*3*8*7)/4! but apparently that is incorrect.
Let me know if you can offer any help.
Thanks!
There are $3$ categories for the $4$ book choices.
$2B + 2N = \binom{4}{2}\cdot \binom{6}{2} = 90$
$3B + N = \binom{4}{3}\cdot 6 = 24$
$4B = 1$
Hence the number of selections is $115$