There are 9 subjects in eighth standard but there are only 6 periods in a day. In how many ways can the time table be formed?

Options

A. 60480
B. 23460
C. 56780
D. 61280

Answer

To solve the problem of forming a timetable with 9 subjects and only 6 periods in a day, we can follow these steps:

### Step 1: Understanding the Problem
We have 9 subjects and we need to choose 6 subjects to fill the periods in the timetable. The order in which we choose these subjects matters because each period is distinct.

### Step 2: Choosing the Subjects
For the first period (P1), we can choose any of the 9 subjects.

- **Choices for P1:** 9 options

### Step 3: Filling the Next Periods
Once we have chosen a subject for the first period, we have one less subject available for the next period.

- **Choices for P2:** 8 options (since one subject has already been chosen for P1)
- **Choices for P3:** 7 options (since two subjects have been chosen for P1 and P2)
- **Choices for P4:** 6 options
- **Choices for P5:** 5 options
- **Choices for P6:** 4 options

### Step 4: Calculating the Total Number of Ways
To find the total number of ways to arrange the subjects in the 6 periods, we multiply the number of choices for each period together:

\[ \text{Total Ways} = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \]

### Step 5: Performing the Calculation
Now, we compute the product:

\[ 9 \times 8 = 72 \]
\[ 72 \times 7 = 504 \]
\[ 504 \times 6 = 3024 \]
\[ 3024 \times 5 = 15120 \]
\[ 15120 \times 4 = 60480 \]

Thus, the total number of ways to form the timetable is **60480**.

### Final Answer
The number of ways the timetable can be formed is **60480**.

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