Four students, Rahul, Mia, Mila, and Andres, line up one behind the other. How many different ways can they stand in line? $\newline$ Answer:

Full solution

Q. Four students, Rahul, Mia, Mila, and Andres, line up one behind the other. How many different ways can they stand in line?

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Answer:

Identify $n$ : To determine the number of different ways the four students can stand in line, we need to calculate the number of permutations of the four individuals. A permutation is an arrangement of all members of a set into some sequence or order. Since there are no restrictions given, we can use the formula for permutations of $n$ distinct objects, which is $n!$ ( $n$ factorial), where $n$ is the number of objects to arrange.
Calculate $n!$ : First, we identify the value of $n$ , which is the number of students. There are $4$ students: Rahul, Mia, Mila, and Andres. So, $n = 4$ .
Find factorial of n: Next, we calculate the factorial of $n$ , which is $4!$ ( $4$ factorial). The factorial of a number is the product of all positive integers less than or equal to that number. Therefore, $4! = 4 \times 3 \times 2 \times 1$ .
Perform multiplication: Now, we perform the multiplication to find the value of $4!$ . So, $4! = 4 \times 3 \times 2 \times 1 = 24$ .
Final result: The result of $24$ represents the total number of different ways the four students can stand in line.