A question paper has two parts, part A and part B, each containing 10 questions. If the student has to choose 8 from part A and 5 from part B, in how many ways can he choose the question?

Answer

To solve the problem of how many ways a student can choose questions from two parts of a question paper, we can break it down into the following steps:

### Step 1: Identify the choices
The student needs to choose:
- 8 questions from Part A (which has 10 questions)
- 5 questions from Part B (which also has 10 questions)

### Step 2: Calculate combinations for Part A
To find the number of ways to choose 8 questions from 10 in Part A, we use the combination formula:
\[ \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
Here, \( n = 10 \) and \( r = 8 \):
\[ \binom{10}{8} = \frac{10!}{8!(10-8)!} = \frac{10!}{8! \cdot 2!} \]
This simplifies to:
\[ \binom{10}{8} = \frac{10 \times 9}{2 \times 1} = 45 \]

### Step 3: Calculate combinations for Part B
Next, we calculate the number of ways to choose 5 questions from 10 in Part B:
\[ \binom{10}{5} = \frac{10!}{5!(10-5)!} = \frac{10!}{5! \cdot 5!} \]
This simplifies to:
\[ \binom{10}{5} = \frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1} = 252 \]

### Step 4: Calculate the total number of ways
Since the choices from Part A and Part B are independent, we multiply the number of ways to choose from each part:
\[ \text{Total ways} = \binom{10}{8} \times \binom{10}{5} = 45 \times 252 \]
Calculating this gives:
\[ 45 \times 252 = 11340 \]

### Final Answer
Thus, the total number of ways the student can choose the questions is:
\[ \boxed{11340} \]

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