Explanation:
7 novels, 3 plays, 4 poetry books and 4 nonfiction, and rounding to the hundredths is rounding to the second number after the decimal point.
the teacher must chose 9 of them, and the restriction is no more than 3 novels. Because the restriction is only in the novels, all the other types are the same in our eyes, this is:
7 novels, and 11 others.
if we put 3 novels.
we have 3 sockets where in the first socket we have 7 options, in the second 6, and in the third 5. this is 7*6*5.
and we have 6 sockets (for the other books) where in the first we have 11 options, in the second 10, and so on. So the total combinations are 11*10*9*8*7*6.
combined are: (7*6*5)(11*10*9*8*7*6) = 210*332640=69854400= (there are a lot of combinations)
if we put two novels, the calculus are similar to before; we have 7*6 combinations for the novels, and 11*10*9*8*7*6*5 combinations for the others, combinating them we get: (7*6)*(11*10*9*8*7*6*5) which is the same number as before, this time the "5" is in the right parenthesis.
then for two novels we got combinations.
And for 1 novel:
For the novels we have 7 combinations, and for the others we have:
11*10*9*8*7*6*5*4, and combinating them we get:
7*(11*9*8*7*6*4*5*4) = 46569600 =
for 0 novels we get only combinations of the other 11 books, so the total combinations are : 11!/2! = 11*10*9*8*7*6*5*4*3 = 19958400 =
So the total combinations will be the sum of the combinations for 3 novels, for 2 novels, for 1 and for 0 novels, this is:
N = 6.99*10^{7} +6.99*10^{7} + 2*10^{7} + 4.66*10^{7}
N = 20.64*10^{7} = 2.064*10^{8} is the total number of reading schedules.