The library is to be given 10 books as a gift. The books will be selected from a list of 23 titles. If each book selected must have a different title, how many possible selections are there?
A) $1,144,066$
B) $4.151586701 \mathrm { e } + 12$
C) $7.124122779 \mathrm { e } + 15$
D) $2.585201674 \mathrm { e } + 22$

Question

The library is to be given 10 books as a gift. The books will be selected from a list of 23 titles. If each book selected must have a different title, how many possible selections are there? 
A) $1,144,066$
B) $4.151586701 \mathrm { e } + 12$
C) $7.124122779 \mathrm { e } + 15$
D) $2.585201674 \mathrm { e } + 22$

Quizplus · Accepted Answer

The number of ways to select 10 books out of 23, with each book having a different title, is calculated using the combination formula $C(n, k) = \frac{n!}{k!(n-k)!}$, where $n$ is the total number of items (23 books), $k$ is the number of items to choose (10 books), and "!" denotes factorial. Thus, the calculation is $C(23, 10) = \frac{23!}{10!(23-10)!} = \frac{23!}{10!13!}$, which equals 1,144,066.

The Library Is to Be Given 10 Books as a Gift