Answer to Question #259740 in Discrete Mathematics for rtf

Question

There are a selection of Action Comics, Superman, Captain Marvel, Archie, X-Man, and Nancy comics.

(a) How many ways are there to select 10 comics?

(b) How many ways are there to select 10 comics if we choose at least one of each book?

Answer 1

(a) The number of ways to select 10 comics is the number of 10-combinations of a set

with 6 elements. 

$$C(6+10-1,10)=\dfrac{15!}{10!(15-10)!}$$

$$=\dfrac{15(14)(13)(12)(11)}{1(2)(3)(4)(5)}=3003$$

(b) The number of ways to select 10 comics if we choose at least one of each book is the number of (10-6)-combinations of a set with 6 elements. 

$$C(6+4-1,4)=\dfrac{9!}{4!(9-4)!}$$

$$=\dfrac{9(8)(7)(6)}{1(2)(3)(4)}=126$$