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

Explanation

To find the number of ways five persons can stand in a row, we can use the concept of permutations. Here’s the step-by-step solution:

### Step 1: Identify the number of persons
We have 5 persons who need to be arranged in a row.

### Step 2: Determine the arrangement process
When arranging these persons, we can think of it as filling 5 distinct positions in a row.

### Step 3: Calculate the choices for each position
- For the **first position**, we have **5 choices** (any of the 5 persons can stand here).
- After placing one person in the first position, for the **second position**, we have **4 choices** left (since one person is already placed).
- For the **third position**, we have **3 choices** remaining.
- For the **fourth position**, we have **2 choices** left.
- Finally, for the **fifth position**, we have **1 choice** (only one person left).

### Step 4: Multiply the choices together
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 5: Calculate the final result
Calculating the above expression:
\[ 5 \times 4 = 20 \\ 20 \times 3 = 60 \\ 60 \times 2 = 120 \\ 120 \times 1 = 120 \]
Thus, the total number of ways five persons can stand in a row is **120**.

### Final Answer
The total number of ways five persons can stand in a row is **120**.

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