There are 3 books of mathematics, 4 of science and 5 of literature. How many different collections can be made such that each collection consists of, one book of each subject.

Options

A. a. 48
B. b. 60
C. c. 168
D. d. 90

Answer

To solve the problem of how many different collections can be made such that each collection consists of one book from each subject (mathematics, science, and literature), we can follow these steps:

### Step 1: Identify the number of choices for each subject
- There are 3 books of mathematics.
- There are 4 books of science.
- There are 5 books of literature.

### Step 2: Determine the number of ways to select one book from each subject
- For mathematics, the number of ways to choose 1 book from 3 is given by \( \binom{3}{1} \).
- For science, the number of ways to choose 1 book from 4 is given by \( \binom{4}{1} \).
- For literature, the number of ways to choose 1 book from 5 is given by \( \binom{5}{1} \).

### Step 3: Calculate the combinations
- \( \binom{3}{1} = 3 \) (You can choose any one of the 3 books)
- \( \binom{4}{1} = 4 \) (You can choose any one of the 4 books)
- \( \binom{5}{1} = 5 \) (You can choose any one of the 5 books)

### Step 4: Multiply the number of choices together
To find the total number of different collections, you multiply the number of choices for each subject:
\[ \text{Total collections} = \binom{3}{1} \times \binom{4}{1} \times \binom{5}{1} = 3 \times 4 \times 5 \]

### Step 5: Perform the multiplication
\[ 3 \times 4 = 12 \]
\[ 12 \times 5 = 60 \]

### Final Answer
Thus, the total number of different collections that can be made is **60**.

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