In how many ways five persons can stand in a row ?

Explanation

To find the number of ways in which five persons can stand in a row, we can follow these steps:

### Step 1: Understand the problem
We need to arrange 5 distinct persons in a row. Each arrangement is considered unique.

### Step 2: Determine the positions
In a row of 5 positions, we can fill each position with one of the 5 persons.

### Step 3: Fill the first position
For the first position, we have 5 choices since any of the 5 persons can stand there.

### Step 4: Fill the second position
Once the first position is filled, we have 4 remaining persons to choose from for the second position.

### Step 5: Fill the third position
After filling the first two positions, we have 3 persons left for the third position.

### Step 6: Fill the fourth position
For the fourth position, we will have 2 persons remaining to choose from.

### Step 7: Fill the fifth position
Finally, for the last position, there will be only 1 person left.

### Step 8: Calculate the total arrangements
The total number of arrangements can be calculated by multiplying the number of choices for each position:
\[ 5 \times 4 \times 3 \times 2 \times 1 \]

### Step 9: Perform the multiplication
Calculating this gives:
\[ 5 \times 4 = 20 \]
\[ 20 \times 3 = 60 \]
\[ 60 \times 2 = 120 \]
\[ 120 \times 1 = 120 \]

### Conclusion
Thus, the total number of ways in which 5 persons can stand in a row is **120**.

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