Question

2 mathematics books, 3 science books, and 5 literature books are required. They are arranged in groups of 3 books each, where each group consists of one book of each subject. How many such groups are possible?

• A. 10
• B. 60
• C. 15
• D. 30

Answer 1

The correct option is D 30

3 mathematics books, 4 science books, and 5 literature books are required.

∴ Number of ways of selecting a mathematics book $={}^2{C}_1=\frac{2!}{(2-1)!\times 1!}=\frac{2!}{1!}=2$

∴ Number of ways of selecting a science book $={}^3{C}_1=\frac{3!}{(3-1)!\times 1!}=\frac{3!}{2!}=3$

∴ Number of selecting a literature book $={}^5{C}_1=\frac{5!}{(5-1)!\times 1!}=\frac{5!}{4!}=5$

So, total number of ways of selecting a mathematics book, a literature book, and a science book = 5 × 3 × 2 = 30