8. In how many ways can 12 books be displayed on a shelf if 15 books are available?: *
A. 455
B. 479001600
C 2.17945728 x 1011
2730
To find the number of ways to display the books on the shelf, we can use the concept of permutations.
In this case, we have 12 books to be displayed on the shelf out of a total of 15 books available. Since the order matters, we can use the formula for permutations:
P(n, r) = n! / (n - r)!
where n is the total number of objects and r is the number of objects selected.
Using this formula, we can calculate the number of ways to display the books:
P(15, 12) = 15! / (15 - 12)!
= 15! / 3!
= (15 * 14 * 13 * 12!)/(3 * 2 * 1)
= 15 * 14 * 13
= 2730
Therefore, the correct answer is option D: 2730.