Question

A librarian choose seven holiday books from a selection of ten to be displayed in the window of the library. in how many different ways can she chose seven books?

Answer 1

Answer:

$_{10}C_7=\frac{10!}{7!(10-7)!}\\\\=\frac{10!}{7!3!}=\frac{10\times 9\times 8\times ...}{(7\times 6\times 5\times...)(3\times 2\times 1)}\\\\=\frac{10\times 9\times 8}{3\times 2\times 1}=\frac{720}{6}=120$

Step-by-step explanation:

A librarian choose seven holiday books from a selection of ten to be displayed in the window of the library. in how many different ways can she chose seven books?

This is a combination of 10 objects chosen 7 at a time:

$_{10}C_7=\frac{10!}{7!(10-7)!}\\\\=\frac{10!}{7!3!}=\frac{10\times 9\times 8\times ...}{(7\times 6\times 5\times...)(3\times 2\times 1)}\\\\=\frac{10\times 9\times 8}{3\times 2\times 1}=\frac{720}{6}=120$