Final answer:
There are 18,564 ways the books can be chosen from the shelf.
Step-by-step explanation:
To calculate the number of ways the books can be chosen, we can use the concept of combinations.
Since we are choosing 6 books out of a total of 18, we can use the formula for combinations: C(n, r) = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items to be chosen.
Plugging in the values, we get C(18, 6) = 18! / (6! * (18-6)!) = 18! / (6! * 12!). It would be impractical to calculate this manually,
so we can simplify it by canceling out common terms in the numerator and denominator: 18 * 17 * 16 * 15 * 14 * 13 / (6 * 5 * 4 * 3 * 2 * 1).
Evaluating this expression, we find that there are 18,564 ways the books can be chosen.