In how many ways can 7 soldiers stand in a queue?

Options

A. A. 5040
B. B. 2880
C. C. 280
D. D. none of these

Answer

To find the number of ways in which 7 soldiers can stand in a queue, we can use the concept of permutations. The number of ways to arrange 'n' distinct objects is given by 'n!'.

Here are the steps to solve the problem:

### Step 1: Identify the number of soldiers
We have 7 soldiers.

### Step 2: Understand the arrangement
We need to arrange these 7 soldiers in a queue. This means we are looking for the number of permutations of 7 distinct soldiers.

### Step 3: Use the factorial formula
The number of ways to arrange 'n' distinct objects is given by the formula:
\[ n! = n \times (n-1) \times (n-2) \times \ldots \times 1 \]

For our case, we need to calculate \( 7! \):
\[ 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \]

### Step 4: Calculate the factorial
Now, let's calculate \( 7! \):
- \( 7 \times 6 = 42 \)
- \( 42 \times 5 = 210 \)
- \( 210 \times 4 = 840 \)
- \( 840 \times 3 = 2520 \)
- \( 2520 \times 2 = 5040 \)
- \( 5040 \times 1 = 5040 \)

Thus, \( 7! = 5040 \).

### Step 5: Conclusion
Therefore, the number of ways in which 7 soldiers can stand in a queue is \( 5040 \).

### Final Answer:
The answer is \( 5040 \).

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